You're certainly right that Amazons featured very prominently in Ancient Greek art and mythology. Everyone from Achilles to Alexander the Great is said to have battled Amazons; Theseus, the mythical king of Athens, supposedly married one. Amazons appear all through the iconographic record, in sculpture, and in literary sources like Herodotos. All this material gives us at least some clues as to why the Greeks were so fascinated by Amazons.

The origin of the myth is likely to be the actual practice of the peoples commonly referred to as Skythians or Sarmatians, living north of the Black Sea. According to Herodotos, their women were warriors. We might normally be inclined to dismiss this as a typical Greek fantasy about foreign peoples, but archaeology confirms the story: graves have been found in the area in which females were buried with weapons, and some female bodies show traces of wounds received in battle. Greek settlement on the Crimea brought Greeks into contact with the Skythians, and stories about warrior women presumably started circulating fairly soon.

This is not to say that the Greeks didn't have warrior women of their own. Female burials with weapons also (if rarely) occurred in early Greece; the goddess Athena was famously armed and dangerous; there were also real-life stories like Telesilla's valiant defence of Argos against the Spartans in 494 BC. However, these fighting women had one major disadvantage compared to the Amazons: they weren't foreign.

Art and mythology leaves us with a clear impression that Amazons were supposed to represent the ultimate other. They were depicted as generic barbarians, often indistinguishable in dress and armament from Skythians and Persians. They were women, but said to be the equals of men, which no Greek women supposedly ever were. They were able to go toe to toe with even the greatest Greek heroes. Their society, as sketched by the Greeks, was an inversion of Greek social norms, with women holding political and military power while men weaved and nursed children at home. Much of the fascination with Amazons likely comes from their nature as the most extreme, unthinkable example of role reversal.

However, it is probably no surprise that just about every story about Amazons involves them being beaten and subjected by men. It almost seems a rite of passage for Greek heroes to prove their masculinity by defeating, controlling or sexually dominating Amazons. Despite the number of images showing Amazons in combat, it is nearly impossible to find any depiction of an Amazon killing a Greek man; the common picture goes the other way around. Indeed, in this sense the Amazons fit into a larger pattern: the majority of Greek mythological antagonists were women, agents of disruption and disorder who had to be either crushed or forced to conform to a male-dominated social order.

In short, the Greek obsession with Amazons probably started with fascination by the customs of barbarians who came to represent the pinnacle of non-Greekness, but was soon co-opted and reinforced by a desire to control women and preserve the existing social order. Amazons are the aliens from our movies, and also the femmes fatales, the rule-breaking, gender-role-defying badasses - but in Greek stories, they always lose.