Gothic has multiple meanings, so the answer to your question is not entirely straightforward. Its potentially relevant meanings (in ascending order of spookiness) are:

--A style of architecture in Western Europe prominent from about the mid 1100s to the late 1500s characterized by big windows, pointed arches, rib vaults, and flying buttresses. This was called Gothic by people who did not like it, but the name stuck.

--Revivals of that style of architecture starting in the mid 1700s.

--Features of the medieval period in Western Europe that were seen as backwards: torture, superstition, religion defeating reason, arbitrary justice, etc.

--A literary genre originating in the 1790s that featured elements of that negative view of the Middle Ages (see above) and might be seen as a particularly dark expression of romanticism.

Some of these meanings are opposed. Most notably, the original medieval Gothic architecture was not supposed to be dark or spooky, but some later audiences perceived it as such, either directly or through association with other features of the medieval world.

Let's talk about medieval Gothic architecture, of which you can find many examples. We actually do know what the intent of this style was, not just from inference but from written sources such as the writings of Suger of St. Denis. He was the patron of one of the most notable early Gothic structures the abbey church of St. Denis which is a suburb of Paris. According to Suger, the fundamental purpose was to let more light into the building to provide for a more edifying experience. And if you visit some Gothic structures you may be shocked by how light the stonework is, how huge the windows are, how much light pours in.

People at the time did not call this style of architecture Gothic. To the extent they distinguished it from other styles, they called it "new" or "French."

The Gothic label for this style was devised by the style's enemies: Italians in the early 1500s whose architectural tastes were shaped by what they considered pure classical forms. Giorgio Vasari is the most notorious example. Vasari and others imagined that the architecture they did not like had been created by "barbarians" such as the Goths (an actual historical people who had practically nothing to do with Gothic architecture) and represented a break with good Roman traditions. These Italian writers themselves believed they were in the midst of a Renaissance of classical civilization and wanted all this medieval barbarism, including Gothic architecture, out. In particular, they didn't want new buildings in this style to be built in Italy.

The name Gothic stuck and was applied in the following centuries by writers across Europe to discuss this architecture, even if they kind of liked it or at least appreciated it. On the other hand, some writers, mostly had a negative view of the Middle Ages applied the term Gothic to all sorts of things they imagined had gone on during these centuries: torture, tyranny, death and disease, irrationality etc. It's all so Gothic!

Starting in the mid 1700s there were a series of Gothic Revivals in architecture: people consciously tried to build new buildings that looked like medieval ones. In addition, during the 1800s we see serious attempts at restoring surviving Gothic structures (including St. Denis), which involved further identifying and purifying the form. As part of the serious restoration efforts, a distinction was drawn between Gothic and Romanesque medieval architecture. The latter featured smaller windows, rounded arches, barrel vaults, and thick walls to support the roof rather than flying buttresses. Romanesque was chosen because of the perception that these techniques marked a continuation (albeit with less skill) of Roman building techniques. It's not Roman but it is Romanesque. The people who used this terminology understood that Romanesque preceded Gothic and was in many ways less technically accomplished than Gothic.

In addition, a genre of literature based on the concept that the Middle Ages were dark and irrational time flourished: Gothic literature. A Gothic novel may not be set in the Middle Ages but it probably contains elements that were considered medieval: it is set in a medieval building or its ruins, the plot involves a curse dating to medieval times, or just the presence of things considered "medieval" such as superstition, torture, or heavy-handed religion. Gothic novels characteristically involved some element of mystery or fright: haunted ruins, monstrous creatures, a mysterious handsome man turns out to have murdered his wife, medieval superstitions turn out to be true, an evil Catholic priest has his way with the heroine, etc. Ruins (of medieval structures, obviously) and torture are really big in Gothic literature. This is also a period in which you see a lot of medievalism (cultural riffing on history) going in various directions.

The use of Goth or Gothic to represent dark, gloomy, or morbid elements continued. Thus in the late 20th century we have Gothic rock and its fans, the original Goth subculture.

All these things feed on each other so some Gothic revival architecture was designed with consciousness of the idea that people associated the style with the motifs found in Gothic literature. The owner or architect might throw in some scary gargoyles or a basement suggestive of a dungeon. A cool feature of Gothic architecture to some revivalists was finding it in a quasi-ruined state, so sometimes features suggestive of ruin were thrown in.

Notre Dame de Paris, the cathedral on the Ile de la Cite in Paris, provides an example of the two trends flowing together. The church is a significant example of the medieval Gothic style. In 1831, Victor Hugo wrote a Gothic novel called in French Notre-Dame de Paris and in English The Hunchback of Notre Dame. The novel is set in the late 1400s--so the Middle Ages--and involves Gothic elements such as witchcraft accusation sponsored by the church, a character with physical deformities, superstition and prejudice standing in the way of love, and of course torture. (Hugo is French and liberal so love and reason triumph; an English author might have treated the subject quite differently.) Now part of why Hugo wrote the book in the first place was to make the reading public fall in love with the building, which he wanted to have restored. In this, Hugo was successful: Notre Dame was spectacularly restored, the area around it was cleared, and it became a landmark of Paris, a must-see for tourists and a national treasure. But notice that Hugo wrote a Gothic novel ("bad" Middle Ages) to promote the restoration of a Gothic cathedral ("good" Middle Ages).

So this is a long way of saying that you aren't the first person to find Gothic structures suggestive of spookiness, but it's possible you see them as spooky because of later cultural associations, because that is the opposite of what medieval Gothic architecture was intended to convey.

Medieval Gothic architecture (that is, northern European ecclesiastical architecture from the mid-twelfth to late-fifteenth centuries) wasn't designed to be scary in the sense of being eerie or ominous, but was designed to be awe-inspiring and to make people feel as if they were in the presence of God. So in that sense, they were supposed to be frightening, if not "scary" exactly. But they were mostly intended to be beautiful - medieval cathedrals and churches would have been filled with light and colour, with wall paintings, sculptures (also painted!), and stained glass. The architectural innovations that allowed for pointed arches, huge windows, and thin columns were used to maximise the light in churches and make them feel weightless. The way we encounter medieval buildings today is very different - when you visit a medieval cathedral there will rarely be much surviving paint, and the walls are often black from centuries of soot from candles. So we end up imagining cathedrals as dark and gloomy, when they wouldn't have been at all!

The Sainte-Chapelle in Paris is a good example - it was built between 1238 and 1248 to hold the Passion relics collected by Louis IX of France and serve as a royal chapel, and is really indicative of the classic French Gothic style. It was almost destroyed during the French Revolution, and lost most of its wall paintings and the bottom two meters of windows, but was restored relatively accurately in the mid-nineteenth century, and it really demonstrates how the amount of detailed decoration in medieval churches would have been totally overwhelming. A scholar and university professor called Jean de Jandun wrote about it around about 1327, and described the chapel as "that most beautiful of chapels," that made someone going up from the lower chapel to the upper one feel as if they had been "rapt to heaven." Thirteenth century cathedrals are more imposing and wouldn't have been quite so densely decorated as the Sainte-Chapelle because of their size, but were similarly intended to be representations of heaven on earth, like Chartres, Amiens, or Canterbury. The sculptures of the Last Judgment on earlier churches like Autun, on the other hand, were absolutely meant to be terrifying so you can see that when medieval artists wanted to scare people, they did not fuck around.

Someone with more expertise on eighteenth and nineteenth century history might be more helpful in explaining why beautiful Gothic architecture became seen as spooky, because you certainly aren't alone in thinking that! My guess would be that from the Renaissance onwards, medieval architecture became seen as barbaric, irrational, and unenlightened, compared to the classical architecture of Italy (following Giorgio Vasari, who was one of the first to describe thirteenth century architecture as "Gothic," since it was "barbaric and monstrous"). By the late eighteenth century, especially in England, it was associated with things that were strange, irrational, or (even worse) Catholic. A lot of old monasteries had also been turned into homes, and the idea of having some old medieval ruins lying about the place was seen as very Romantic and poetic. Hence Gothic literature (and then films) being set in crumbling old abbeys, or ancient castles in scary Catholic countries (a la Dracula), and making Gothic associated with horror.

Some good sources for starting to read about Gothic architecture, if you're interested:

Paul Binski, Gothic Wonder, Becket's Crown

Erik Inglis, "Gothic Architecture and a Scholastic: Jean de Jandun's 'Tractatus de Laudibus Parisius' (1323)," available on JSTOR

Robert Branner, Gothic Architecture, St Louis and the Court Style in Gothic Architecture

For medieval aesthetics generally, I would highly recommend anything by Mary Carruthers - she's brilliant and surprisingly accessible, and most of her articles are available for free on her Academia.edu account. I would particularly recommend for this question her article "Terror, Horror, and 'the Fear of God'" and her book The Experience of Beauty in the Middle Ages.

There is also the new book The Bright Ages by Matthew Gabriele and David Perry which is intended to be a general introduction to medieval studies, I haven't read it yet so can't recommend it with confidence, but Matthew Gabriele is a wonderful scholar.

This was all from memory and it's my first time posting on this sub, so apologies for being either too vague or too rambling! If you are interested in medieval spooky things though, I can provide more sources if you like - my real area of expertise is scary medieval sculpture!

I’d very much like to see a comment from a social/literary/film historian about the path that gothic revival architecture took to become the de facto “haunted house”. Why this style and not Greek revival or Georgian buildings? Did Disney choose this style for their Haunted Mansion because this was already shorthand for “haunted house” or did Disney’s choice create the idea that Gothic revival was more “scary” than Tudor revival, etc. houses?

u/eros_cestlavie does an excellent job of succinctly covering the importance of light in medieval Gothic churches and the intention of their builders to provide an uplifting experience of spiritual space to complement the increasing veneration of the Virgin Mary as a nurturing and merciful intercessor.

But if the medieval Gothic is so closely linked with religious transcendence, where then does the connection between Gothic architecture and horror come from? Our contemporary view of Gothic architecture owes more to the style’s revival during the 18th century than to its emergence in the 12th century. The modern Gothic Revival led to the construction of imitative designs throughout the world and to the application of the Gothic style to buildings beyond ecclesiastical and scholastic structures (as well as the imaginative restoration of many medieval Gothic buildings). Our contemporary perception of the Gothic owes less to the original medieval buildings than to this modern interpretation, one which was heavily influenced by the philosopher Edmund Burke and his notion of the sublime as the aesthetic antithesis of beauty.

The renewed interest in the Gothic style beginning in the late 17th century corresponded with the nascent Enlightenment’s fascination with perception, sensation, and emotion, as is evident in the philosophy of René Descartes and John Locke. In this period, architecture moved beyond the pursuit of ideal proportions and divine perfection to incorporate other considerations such as individual experience and feeling. As a result of this epistemic shift, new styles divorced from the Classical principles of symmetry and regularity developed, which included the Rococo and the picturesque. Non-European architecture was reappraised, and long-neglected historical styles were rehabilitated.

In 18th century Britain, the decayed ruins left after the Reformation and the Dissolution of the Monasteries gained new value for their gloominess and melancholic associations, which were echoed by poets like Thomas Gray. Medieval Gothic ruins scattered across country estates inspired garden designers like Batty Langley, who used them as a decorative backdrop for their landscapes as well as a source of inspiration for newly constructed pavilions, shelters, and summerhouses. Among the earliest to recognize the architectural potential of the Gothic style in the 18th century was Horace Walpole, who constructed a house at Strawberry Hill in Twickenham beginning in 1749. Strawberry Hill embraced the variety of Gothic ornament—all of the trefoils, quatrefoils, and pinnacles—and the irregularity of the Gothic floor plan.

At Strawberry Hill, Walpole replicated and recombined existing elements from surviving examples of the Gothic style throughout Britain, producing an inspired and original combination of architectural fragments that was much imitated in the following decades. Walpole’s other contribution to the Gothic Revival came in the form of a novel said to have been inspired by a nightmare he had while living at Strawberry Hill: The Castle of Otranto, published in 1764. Walpole’s novel, the first of many in what became known as the Gothic genre, sought to capture a feeling of terror and wonder. This feeling—of the sublime—was also analyzed in the philosophical texts of Edmund Burke.

Writing in the middle of the 18th century, Burke offered up the sublime as an alternative aesthetic category capable of provoking madness, delirium, and horror in place of the love, passion, and desire stimulated by beauty. Beauty, as reflected in the clarity and legibility of Classical architecture, could be complemented by the magnificence and mystery of sublime Gothic architecture. Burke was quite explicit in defining the characteristics required for architecture to provoke sublimity: extremes of scale, height, shadow, and light. These criteria were to guide the design of late 18th century Gothic Revival architecture.

Perhaps no building captures the dogged 18th century pursuit of sublimity better than Fonthill Abbey, commissioned by William Beckford and designed by the architect James Wyatt. Fonthill Abbey was a domestic cathedral, featuring 68-foot-tall doors and a 300-foot-long central transept. A sense of foreboding dominated the house and proved to be prescient when, in 1825, the building’s 278-foot tower, which was built at great speed on faulty foundations, collapsed just 13 years after its completion. But while Beckford and Wyatt may have stumbled in their desperate grasping at the sublime, they did manage to complete the circle by producing their own romantic Gothic ruin.

During the 19th century, the appreciation of the Gothic style would shift from sublimity to focus variously on its structural innovations, Christian symbolism, nationalistic connotations, and potential as a model for social reform. But the association of Gothic architecture with the sublime and all things that are dark, mysterious, and—yes—scary would persist and, indeed, thrive through its representation in literature. The works of Edgar Allen Poe, Bram Stoker, and many others would cement the association of the Gothic style with horror in the contemporary mind.

SOURCES:

Edmund Burke. A Philosophical Enquiry into the Origin of our Ideas of the Sublime and the Beautiful. London: R.& J. Dodsley, 1757.

Kenneth Clark. The Gothic Revival: An Essay on the History of Taste. London: John Murray, 1962.

Michael Lewis. The Gothic Revival. London: Thames & Hudson, 2002.

Horace Walpole. The Castle of Otranto. London: Tho. Lownds, 1765.