This might sound like I'm being daft, but the answer you get will differ, sometimes significantly, based on who you ask. There's an entire school out there who believes that the West's economic primacy was pure happenstance. Me? I'm an institutional development theorist with a cautions bit of environmental determinism and constructivism thrown in. Here's my take; and yes, I will bending the rules a bit, because the jury is absolutely not in for development theory, and I need to qualify that I'm more than happy to talk about factors that I might have missed. Plus, those are two completely different periods of history, I can't cover everything on a Reddit post.

In fact, I can't pretend to be able to accurately explain the history of culture in the world, or the history of culture in Italy, for that matter. And I'm certainly not about to try. But I can take you through some simple ideas that might flesh out your understanding. Just a warning, we will be dealing with generalizations. Generalizations can be dangerous if taken to lightly or interpreted to be all-encompassing; understandably historians prefer to focus on details, But generalizing really the only way of answering a broad question like yours. Although I will defend my statements, each one is a topic of debate and I'd be happy to explore individual nuance more in depth.

So, let's begin in the beginning: initially, many great ancient civilizations emerged in river valleys. The Yellow River and the Indus in Asia, the Tigris and Euphrates in Mesopotamia, and the Nile in North Africa; all these rivers saw the rise of complex, agriculture-based empires on their banks. Prior to the Iron Age, Italy can not be called a prime candidate to develop this kind of society; Italy is a narrow, mountainous peninsula, whose rivers; the Po, the Arno, the Tiber, and the Volturno, are in no way comparable to the great rivers of the world, even if as we'll see later they're pretty darn fertile nonetheless.

However, innovations soon spread north and westward across the increasingly busy sea-lanes of the Mediterranean. As trade grew, on the rocky Greek peninsula it became less imperative for food to be grown walking distance from where people live. Greece (or rather, first Phoenicia, and then Greece) developed a complex society based in autonomous, highly competitive mercantile city-states. Some of these city-states founded colonies to the west; but autonomous city-states also sprung up independently in Italy (however, up to the early Iron Age these early Italians are still very much on the periphery of the more complex societies to the east).

The extremely competitive Greek city states pushed each other to innovate. If you look closely, there is no other similar place in the world where small, urbano-centric polities can easily carve out convenient geographically defined spheres of governance. Intense trade between the Greek cities allowed innovations to spread, and actors on the Greek periphery could would elaborate these innovations further. Indeed, "catch-up" by the periphery is an interpretation I rather like in Economic History; it's first observable with Greeks, who I think create a more "inclusive" society supporting what is closer to our conception of an economy when compared to the nearby Egyptian and Mesopotamian Empires, where the central power of the state —sometimes seeped in mystic religiosity— has a tighter control on things like trade and agriculture. But where I think we see an even stronger example is with regards to the peripheral Greek state of Macedon, whose military and social innovations allowed it to first dominate all of Greece, and then construct a massive empire encompassing the whole of Egypt and Mesopotamia. There's also a "Power-Cycle" lens (which I also find kind of nifty) you could use to supplement this whereby the reasoning goes that after a long series of innovations, the barriers to innovate further are too high and a previously innovative society starts to comparatively decline as the slack is picked up by a more peripheral society with fewer inhibitions.

Now, looking at the history, it is tempting to say that had Alexander the Great not died in his thirties, we might speak of a pan-European Macedonian Empire, and not a Roman Empire. However, this sort of history emphasizing the role of a "Great Man" fell out of favor a long time ago. It is more accurate, explained one of my professors, to think of history as a great torrential river, where great men are those who are most skilled at paddling their canoe along with the current. Alexander constructed a great empire, but did he have the social, political, and economic tools at his disposal to guarantee its survival past his death? Probably not.

The importance of Greece in laying he groundwork for western society cannot be understated, but if we talk of "Europe" at all, it's because of events that happened in Italy. Initially even more peripheral than Macedon, the city-state of Rome, in increasingly strong dialogue with Greece as trade links across the Mediterranean kept growing, developed an even more elaborate political system as it federated a multitude of peoples in Italy. Was the rise of Rome inevitable? Of course not. I myself would have put my money on one of the Greek colonies farther south; this much I will concede to happenstance. However, the important take-away is that Italy was a peninsula where people could apply Greek-inspired ideas on a territory more inductive to developing territorially larger polities; in short, the periphery figured how to apply ideas developed by the core, and found they are better at them.

Italy is a fertile peninsula jutting out into the Mediterranean. Was an Italian state, fundamentally what the Roman Republic was just prior to the Punic Wars, predestined to conquer Europe? No, of course not. But if anyone was going to unify Europe, it would have been them. And, if five hundred years of Empire are anything to go by, I think they were pretty darn successful. There were very many factors contributing to Roman success, but I think the simplest is that geography is important: Rome is in the middle of the peninsula in the middle of an inland sea. And that peninsula is a lot more agriculturally productive than the neighboring two peninsulas.

Of course, we should take a moment to distance ourselves from our absolutes. Greece remained a prosperous, urbanized, and influential region even when conquered by Rome. So much so that when the Roman governing system imploded in the fifth century, the political power system had long since completed its migration to Greece! But in spite of Greece's important position within the Empire, it's impossible write off Italy as the focal point after the Roman Empire creates a sort of common Mediterranean trade area.

There's also a whole discussion to be had on the extent of institutional continuity after the ruler of Italy stopped calling himself "Imperator" in favor of "Rex Italiae." If you really wanted to, you could even read the entire period between the fifth and eighth centuries as a struggle by Italian elites to decouple their power system from Greece, the other Mediterranean focal point. In the end, although a united Italy had easily subjugated Greece, it would seem that Greece, although also united, could not achieve the subjugation of Italy (although it could do other things, like defend itself from hostile eastern neighbors. However I've always been more partial to a narrative in favor of a declining post-Roman Greece, with several notable resurgences, of course).

I would argue that throughout the bumps and kinks in the road (including but not limited to the brief subjugation by an empire in Northern Europe, a period of utter political instability, and brief but recurring armed confrontations with Germany) the Italian peninsula continued to be the focal point of Mediterranean trade, and most importantly, retained the institutions which were borne out of this trade. And for this reason I don't really like the word Renaissance, nor am I enthusiastic about its periodization; I think that Italian artistic and social history exists on a continuum, with spurts of growth in the thirteenth and eleventh centuries comparable to those in in the fifteenth. The "Renaissance," such as we know it, is in my view the last great period of economic growth until the larger nation states of Western Europe begin exploiting the Atlantic trade, and Italy stops being the master of its destiny.

Whew. I wrote a whole lot while saying very little. This was a difficult thread to tackle; I might have raised more questions than I answered.

Edit: I accidentally lots of words