There are several things that are incorrect with your analysis of art in the early days. The bust you posted is sculpture, which is inherently 3D. During the High Roman period, sculpture was well developed however painting (and mosaic) was not as refined in terms of perspective and dimension. As this image of the wall of the Villa of Mysteries in Pompeii shows, the 3D representation of figures and naturalism was lacking during this period. After the fall of the empire, there was an under-funding of art and the sole funding came from the church, which was not quite as interested in new artistic movements and perspectives as it was in getting their religious images down. Hence, early Christian iconogrophy, which is what your images show, were not revolutionary in terms of painting. During this time, however, there was still very accurate perspective in sculpture, both bust and relief.

Indeed, the first revolutionary perspective on artistic representation in painting did not come about until Alhazen who, in 1021, wrote a book on optics and color theory. These theories were then used to kick start the Renaissance artistic movements when Brunelleschi used them to invent linear perspective, allowing accurate 3D representation on a two dimensional canvas. At this point it is important to note that the Renaissance artists had money and time to experiment with new forms of representation, allowing them to push away and discover these three-dimensional works.

Finally comes modern art (my specialty). Modern art is characterized by a vastly different meaning that art of antiquity. As you correctly pointed out, modern art is artistically motivated. This means that modern art is art for the sake of being art. They no longer have to worry about funding from the church or from political kings and emperors (the only supporters of the arts during the medieval period). This freedom gave artists tremendous freedom of exploration and of expression. At this point art movements diverge and evolve much more rapidly. The Impressionists arise with a theory that we, as humans, see the world as it makes an impression on us. We do not all see the same thing, rather, we all see it from our own perspective (almost like an early theory of relativity, stating that the world is relative to the viewer). In this manner they independently set out to paint what impression they got from their motifs.

Modernism is itself a different era of art. It is very broad, and it is hard to specify what makes modern art modern, other than it is modern because we say it is. To better give you some perspective, I will focus on one specific artist: Piet Mondrian and the movement he created: Neo-Plasticism. Take a look at this painting by Mondrian. This is his first "abstract" work, Composition 10 in Black and White (also known as Pier and Ocean). It took Mondrian 2 years of research and trial to come up with this, his first abstract painting in 1915. (I say abstract in quotes because we can still make out his motif, the pier and the ocean and the stars). Later on, Mondrian develops his theory of form and color further and comes up with this, Composition with Grid 9, in 1919. Truly abstract, we no longer see a motif. Finally, by the end of 1920, he had developed Neo-Plasticism. It is hard to explain why this is revolutionary and redefines art without seeing it in person. These paintings are very large, yet there is a simplistic balance when looking at them. The color, the form, the balance is what makes a Mondrian a Mondrian. Piet has moved away from realism and towards idealism. He is not depicting the natural world, he is depicting and idea, but that does not make his depiction any less real. He wrote prominently about art and color theory during this breakthrough. And he was not funded by the Church, though he was influenced by Theosophy. He truly redefined art in a way the Medieval painters did not.

Source: Art Since 1900

MoMA, The Collection, Theme

This line:

ot to Modernism, he explained the shift from a Naturalized portrayal to an abstract one as these artists being geniuses who were tired of just depicting the realistic world and shifted to a new way of painting. Why does there seem to be such a bias favoring the modern painters for redefining art, but not the Medieval ones? Were they that different?

Suggests to me that what you are really after is not so much a question on the history of medieval painting and the vexed question of realism in painting(and it is almost axiomatic, at least to me, that different artistic epoches will produce different methods and techniques of painting according to the goals of artists and art-buyers, whether those buyers are churchmen, civic bodies, private individuals, or museums, as you seem to correctly deduce, and "realism" is a rather problematic term itself, being constantly redefined by what has come before and what will come after) as a question on the historiography of medieval and byzantine art, that is the history of its understanding and reception. This is actually a very interesting and complex topic, which I will break down into several periods: the immediate post-medieval era, from about 1550-1750, the romantic and revivalist approach to medieval art from about 1750-1870, and our present historical approach. These boundaries are of course fuzzy and each period's history is shaped by the reception of medieval art in previous periods, but it is still I think a useful framework.

The point from which I want to start is about 1550 for a specific reason, namely that this is when Vasari's first edition of Lives of The Artists came out. Vasari's work is remarkable because it is the first work of "proto-art history"; that is the first work to describe the development of art in a narrative framework. Now the framework he adopts from his models is essentially of decline and revival, according to which medieval art is to be regarded as the inevitable decline of art that in turn is undone by the Renaissance painters. This framework, which has considerable overtones of both Hesiod's ages and Christian salvation history, cast medieval art primarily as a sort of improverished contrast to Renaissance art. This set the tenor of attitudes towards medieval sculpture, painting and architecture in Italy for an extremely long time. In the north, meanwhile, the influence of the Reformation and Counter-reformation meant that sacred art had become not insufficiently powerful, but too powerful and in need of domestication. Here, the otherworldly qualities of medieval art became linked to abuses and corruption in the institutional church and eventually the entire tradition of image-making was transformed by the decline of church-centered patronage and the adoption of Italian models(itself a story that could encompass a whole post).

This state of affairs remained relatively consistent until what might be termed the medieval revival of the late 18th and 19th centuries. Concurrently with the development of a stricter form of neoclassical architecture that directly looked to Greek and Roman precedents stimulated by the discoveries of Pompeii and Herculaneum and increased interest in the Greek ruins in the Mediterranean an increased interest in medieval architecture developed. This process picked up steam with the full-fledged revival of Gothic architecture as a movement beginning in the early 19th century; at the same time there was an increase in the collection of medieval art at least in the UK. This was not however really a disinterested revivalism, but an intentional project of using medieval art and architecture as a springboard for the critique of classical aesthetics and industrial society. Early theorists of medieval art and architecture consistently stressed its irregularity, variety, and unreality as a project of contrasting it with Classical and Renaissance architecture and framing it as a relic of an age when religious faith and handcrafts provided a unified framwork for human life. An author like John Ruskin, for example when attempting to characterize the essential traits of Gothic architecture is his very popular The Stones of Venice could and did characterize medieval architecture in those terms even though one could easily place regularity and orderliness at the center of Gothic architecture. A similar approach to medieval art produced the inverse effect in the United States, where persistent associations between religious imagery and Catholic "superstition" as contrasted with Protestantism largely scuppered the long-term exhibition of America's first large collections of Medieval Italian painting. In either case, the collecting of medieval art and imitation of medieval architecture and painting(c.f. for example the Nazarenes in Germany) had very specific motivations that in turn shaped how people described and understood medieval art, very often characterizing it as "primordial" and in some cases setting it alongside other examples of art considered exotic or primitive.

Later in the 19th and during the 20th century, the discourse surrounding medieval art was shaped both by the emergence of art history as a formal discipline and by the emergence of modern art starting around 1860. The methods of art history attempted to set medieval art as part of a larger artistic trajectory that could be described by large-scale historical processes. An excellent example of this is Riegl's idea of kustwollen, or "artistic volition", the thesis that the methods of artists are constantly being reshaped by historical processes and demands. They were also shaped by the technology of reproduction; the development of methods of widely and easily disseminating accurate reproductions of art allowed art historians to attempt to study specific periods of art based on a large sample of objects rather than a sort of antiquarian attempt to extrapolate from a handful of objects they could access. Concurrently, the early 20th century study of early Christian art gave medieval and Byzantine art a prehistory; it was no longer a sort of primordial origin but rather a historical moment that sprang out of the historical moment of late Roman art and which had to be accounted for in relation to classical art. This gave rise to both a sort of neo-Vasarianism in which medieval art was seen as a sort of symptom of the degeneracy of the late Roman Empire and medieval Europe(the view your teacher seems to articulate) and an attempt to explain it more positively as an attempt to adapt the methods of Classical art to the needs of Christian theology and devotion. At the same time, however, this approach shied away from pronouncing aesthetic judgements.

Concurrently, students and collectors and patrons of Modern art attempted to articulate a historical narrative that could encompass modern art when the old narrative of realism became outmoded. This is where the conception of artistic freedom became a useful narrative framework. According to this framework, the history of art was the history of the artistic personality gaining liberation from the shackles of convention and repressive patronage (and one can see I think this framework's attraction in a historical period that was and is seen as a time of struggle between political liberalism and authoritarianism). Here, medieval art was contrasted with modern art based on the presumption that it was produced under less free conditions as opposed to the modern artist who did not in principle at least have to answer to the church. Now this framework did not necessarily mean that medieval art had to be characterized as bad, but it did mean that whatever distinctive qualities it had were more or less likely to be seen through this lens.

Hopefully I have at least clarified where and how your teacher's understanding of art history comes from, and how it is itself the product of historical forces even if my historiography of medieval art is itself a limited and incomplete affair. But this process of approaching medieval art in new ways is still ongoing; feminist and queer literatures on art have produced powerful new ways of understanding medieval art as part of the gendering of devotional practice, scholars like Hans Belting(whose book Likeness and Presence I cannot recommend highly enough) have attempted to understand medieval art as a project of making the sacred physically visible and present in new ways, and scholars have attempted to re-examine questions of how medieval images were used and interacted with beyond aesthetic contemplation.

when we got to Modernism, he explained the shift from a Naturalized portrayal to an abstract one as these artists being geniuses who were tired of just depicting the realistic world and shifted to a new way of painting

Yes and no. The main issue with this view of art in the twentieth century is that it takes a heavily [formalist](http://en.wikipedia.org/wiki/Formalism_(art) perspective of the history of art-- that is, being solely focused on the observance and deconstruction of external reality in terms of visual image. This also implies that the primary goal of "modern art" was abstraction, which is false. This brings up the importance of distinction between abstract and abstraction. The former is simply a choice in visual tools that lends to the simplification, deconstruction, or even complete destruction of relatable visual imagery, often to use for whatever the purpose the artist intended. The latter was an actual school of thought, a formalist motivation to study the external world and break it down into the relational bits and bobbles that make an image, or go further and distill it into it's "purest" form. This view is regarded to have been pioneered by artists like Cezanne in the late 1800's, and taken further by the Cubists, Constructivists, Purists, NeoPlasticists, and the American and European Abstractionists.

However, there were a myriad of groups of artists in the 20th century that were not focused on formalist deconstruction of the external-- On the contrary, many were actively working against this highly academic and aestheticized view. In the American scene in particular, critics and artists alike grew tired of the staleness of the Abstractionists around the 40's. Jose Ortega y Gasset in "On the Point of View of the Arts", cited by Irving Sandler in Triumph of American Painting, embodies this view fairly well and believed the progression of art as having 3 main stages:

"First, things are painted; then sensations; and finally, ideas. This means that in the beginning the artist's attention was fixated on external reality; then on the subjective; finally on the intrasubjective".

This attitude is not in itself the truth per se, but is a good representation/example of the general mindset of the era. The idea that simple external visual focus was uncommon. Groups of artists either not focused on the pure formalism of "academic" or "external" abstraction or were actively against it include the Abstract Expressionists, Dada, Surrealists, German Expressionists, Social Realists and a large number of other schools.

These groups utilized the language of the abstract, celebrating the "liberation" from the need to represent. But although the language of abstraction was a common occurrence throughout the 20th century, the formalist stance of unilateral progression of art as having solely to do with matters of the purely visual is ultimately false. Rather, this language was simply another tool for the artist-- unlocked by those whose primary concern was formal, but utilized by many who cared very little for anything of the sort.

Sources: Irving Sandler's Triumph of American Painting