What you are describing is the result of a way of understanding history that permeates practically all public discourse about history, in Europe and America but also almost everywhere in the world. It's become so common that it takes a conscious effort to think differently about history, and often in primary and secondary schools in the US, this is the way that history gets taught. The basic idea has a few different names; it can be called unilinear evolution, or whig history, or universalism, or progressive history, or even just modernism. It developed in the 18th and 19th centuries, and reached a high point in the early 20th century, at the zenith of European imperialism.

Let's explain what is meant by unilinear history. From an anthropologist's perspective, a key text of this particular theory is Morgan's Ancient Society (1877). The thesis of this book is that all human societies exist along a single evolutionary continuum, which you can imagine like a line that slopes upward from left to right. On the lower, left side of the line is "savagery"; in the middle of the line is "barbarism" and at the top is "civilization". These are considered stages through which all human societies must pass. The way that societies develop from one stage to another is through technological advancement, so therefore you can determine which stage a society is at by the technology used. There are even subdivisions-- so American indigenous peoples were considered to be at a stage of "high" savagery, having developed the bow and arrow, while Australian indigenous peoples and Polynesians were considered to be at a stage of "low" savagery, since they did not have bows and arrows. The stage of barbarism includes things like early states and farming societies, with agriculture and iron-working. Finally, "civilization" referred to the most “advanced” societies on the planet at the time— the 19th century capitals of European imperialism, i.e. London, Paris, and Berlin.

What was important about this theory is the idea that all societies had to progress along the line from savagery to civilization. This implied that the European imperial societies of the 19th century had progressed from savagery, through barbarism, to civilization, at different points in the past. Stone Age Europeans, then, were equivalent to 19th century hunter-gatherers living in places like Africa or South America, and it was implied that these people, too, would one day progress to civilization (with the helping hand of missionaries and European colonial rule, of course).

This idea also meant that historians were keen to chart the progression of technological progress (i.e., the progression towards civilization) throughout time. Since 19th century Europe was a Christian world, they looked to the origins of their religion: the Middle East. There they found the earliest evidence for writing and advanced architecture. They surmised that you could chart a progression like this: The earliest Neolithic sites in the Fertile Crescent—> the earliest cities in Mesopotamia, at Ur and Uruk —> the Bronze Age societies of Akkad and Sumer —> the Iron Age societies of Assyria and Babylonia —> … wait a minute, the 19th century Middle East is under European colonial rule and civilization is the sole domain of northern Europe, so lets jump to … —> Classic Greece —> Ancient Rome —> Charlemagne —> France and England in the High Middle Ages — > the Italian Renaissance —> the Enlightenment and Protestant Reformation —> Imperial Britain and France.

In this way, European historians made imperial Britain the inheritor of 4000+ years of movement toward what they saw as the crowing achievement of social progress. There was a HUGE racial / racist element to this, of course, which you can see might be pretty obvious, but I won’t get into here. Notice how the 19th-20th century Middle East is disinherited of the legacy of Bronze Age Mesopotamia— instead, that cultural legacy is thought to flow from the Middle East to Greece to Europe sometime around 500 BC.

Notice also that this progression is basically still the order in which you learn about ancient societies in grade school and high school in the US! And considering this perspective, you can start to see why people reflexively would use the word “we” when talking about ancient Greece— the discourse of historical and cultural progress from ancient Mesopotamia to imperial Europe (and then to America) is extremely prevalent in how we instinctively think about history today, especially at the level of general education.

You learn in grade school in the US that our constitution takes a lot from Athenian democracy. Well, it's not so much that the American constitution was based on Athenian democracy (it's actually quite different), it's more just that the Founding Fathers in America absolutely believed themselves to be the inheritors of civilizational progress that went back to the ancient Greeks (in the 18th century, not much was known about Mesopotamia, so Greece was thought to be the origin of culture and progress), and were keen to perpetuate and emphasize this link.

It took a huge amount of work and theorizing to challenge and subvert some of these views, and to formulate different ways of understanding historical change. Franz Boas’ idea of historical particularism was especially important. This idea said that all societies interact, but that change within a society follows a particular path based on a variety of factors within its own social system and in relation to its environment. Therefore, you cannot chart any evolutionary course that all societies follow, and you can’t compare societies on the basis of “progress” toward any single ultimate aim. Instead, societies should be studied and analyzed according to their own internal logics. In many ways, Boas was an anti-racist for his time— he rejected the idea that non-European societies were inferior, and insisted they were just different, but still internally consistent.