Basically, it’s because that’s the system that 19th-century German historians of the Middle Ages came up with, and English historians then borrowed/translated it:

“German historians, generally followed by their English-speaking counterparts, have tended to differentiate between the Früh-, Hoch-, and Spätmittelalter, or ‘early’, ‘high’, and ‘late’ Middle Age(s). In contrast, historians in Romance-speaking countries prefer to distinguish between the ‘high’ (early) and ‘low’ (late) Middle Ages (in French, for instance, haut and bas Moyen-Age). Hence…in the context of continental historiography it is a very ambiguous phrase.” (Power, pg. 3)

Since it could be confusing to use “high”, English historiography also calls the middle part the “central Middle Ages” (as in the title of Daniel Power’s book).

Power goes on to give some reasons why the “central” or “high” Middle Ages could be considered a high point:

“…Latin Christendom ceased to be on the defensive against neighbouring cultures and began to expand aggressively against them. Secondly, Latin territorial expansion was accompanied by a demographic and economic transformation, vastly increasing the continent’s population, number of settlements, and cultivated land…Thirdly, the second half of the tenth century witnessed several events that recast the framework of Western European politics for several centuries." (Power, pg. 5)

This was also the period of the so-called “twelfth-century Renaissance”, the creation of universities, increasing centralization of the church, etc.

The "high" Middle Ages began to decline with the Black Plague and poorer weather of the 14th century, among other things. The 15th century is the subject of Jan Huizinga’s famous work on the “Autumn” or the “Waning” of the Middle Ages.

Periodization within the “Middle Ages” also sometimes depends on the country or even the individual historian. I bet if we asked all the other medievalists here, we’d come up with as many divisions as there are users! For France, for example, we might divide things from the Merovingians and Carolingians up to the Capetians (6th century-987), the Capetians up to the Valois (987-1328), then the Valois to the Bourbons (1328-1589). But perhaps the “bas Moyen-Age” in France extends all the way up to the Revolution in 1789? In England we might divide the Middle Ages into only two (pre- and post-Norman Conquest in 1066), but there are other possibilities. Other countries will also have their own divisions.

And of course, however we divide it, this three-part system only applies to the western bits of Europe, and not Eastern Europe, or Africa or the Middle East, or anywhere further east in Asia, which all had contact with each other during this period. This is why historians now also often speak of a “global Middle Ages” - rather than focusing on increasingly specific divisions that apply only to a small portion of Europe, emphasis is instead placed on the interconnectedness of the entire African-Eurasian landmass. This is a fairly new trend though, and it hasn't really caught on in the non-academic world yet...

Source:

Daniel Power, The Central Middle Ages: Europe 950–1320 (Oxford University Press, 2006)