My answer deals with a slightly later period, but broadly responds to your question:

It's worth remembering that most of the great philosophers of Ancient Greece were not democrats. An aristocrat educated in classics might therefore be distrustful of (Athenian) democracy more than in awe of its virtues.

The contemporary and popular view of democracy is more a product of enlightenment thinking. Whilst I don't deny that some enlightenment thinkers will have been influenced by their studies of classics, it's a stretch to credit to Greece the modern emphasis on egalitarianism and the mandating/legitimising function of democracy.

I can't really answer this question with certainty, but I can think of a few ways to nuance it or at least offer some different perspectives to think about this from. Hopefully someone better trained in European medieval history can do better.

First of all, where are we talking about? Western Europe or the Byzantine Empire? For large parts of the middle ages, knowledge of Greek was lost in the west, and any knowledge of Greek history and philosophy was transmitted through Latin texts, whether Roman or those written after the collapse of the western Roman empire. In general, the texts that were transmitted were not concerned with constitutional questions. For example, one of the most popular texts dealing with Greek history in the Frankish kingdom of the 7th-10th century was Curtius Rufus's History of the Campaigns of Alexander, which is particularly concerned with how subjects can behave under an monarch (it was written in the Roman imperial period). Texts that are irrelevant to a society's concerns tend not to be transmitted, and ideas about Greek democracy were not incredibly relevant. Meanwhile, although Byzantium's official language was Greek and many Greek texts were transmitted in Eastern Europe, Byzantine rulers (or rulers of the Eastern Roman Empire, as they'd call themselves) were much more concerned with presenting themselves as successors to the Roman empire rather than Greek democracy.

But when knowledge of Greek literature became more widespread, and authors such as Plato and Aristotle were read in the original language throughout Europe... Well, even then, Plato and Aristotle and many other Greek authors are highly critical of Athenian democracy. Aside from the Athenian orators and rhetoricians of the fourth century, very few surviving works directly praise Athenian democracy, which was only one constitutional form among many in the Greek world. Later Greek authors, writing after the conquests of Alexander or the Roman conquest of the Greek city states, also tended to be critical of full democracy.

So again... I wish someone more qualified would answer this, but if I had to guess, I would say that knowledge of Athenian democracy was a lot less widespread among the European nobility than you might think, and that the dominant impression Europeans received of it was negative. Later political thinkers would share this dislike of direct democracy, from Machiavelli to the founding fathers of America, all of whom wanted to establish a state along the lines of the "mixed constitution" of the Roman Republic rather than the constitution of classical Athens.

You have to consider that there where a lot of greek city states and only very few had democracy. Thos who had democracy only had in for some time, before it was overtrown again. So the nobility might have thought that it was a failed idea and that a kingdom/aristocracy was a more stable (better) form of government.