Who were enslaved by the athenians in antiquity? And why were they believed to be suited for slavery?

Taking these as two separate questions:

Athenian slaves seem to have been primarily obtained as prisoners of war, or by purchase from slave traders. Aside from these sources, the children of two slaves would be a slave, and at least in the first century CE the child of a slave and a free citizen woman would be free (although not a citizen). Prior to the seisachtheia of Solon in the early sixth century BCE, there would have been Athenian citizens who became slaves for financial reasons: they might have been sold as slaves by their parents or relatives, or they might have become slaves as a penalty for failing to pay a debt owed. We have no data about the relative number of citizens who suffered this fate, but since Solon explicitly forbade it, I’d feel comfortable assuming it was prevalent enough to be a major concern. Even after the laws of Solon, there were exceptions for specific situations: citizens could sell daughters who had sex before marriage, although this doesn’t seem to have been a common practice by at least the fifth century, and a citizen who was taken captive in war, ransomed, and failed to pay back his ransom would become the slave of his ransomer. Metics (free non-citizens living in Athens) could be enslaved as punishment for various crimes, most of them relating to the metic attempting to do specific things reserved for citizens. When it came to captured prisoners, most of these would have been ‘barbarians,’ although not exclusively. By the fourth century, Plato and others argue that Greeks should not enslave other Greeks, but this should not be meant to mean that it never happened.

As far as believing people to be “suited” for slavery, there are certainly reference to “barbarians” as naturally servile. Most famously, in Aristotle’s Politics, he declares that there are certain kinds of people for whom slavery was a natural state, and those for whom it was a violation. In the context of his times, he classified the Persians as being among the natural slaves, and Plutarch indicates that Aristotle advised Alexander in his campaign to “treat the Greeks as if he were their leader, and other peoples as if he were their master; to have regard for the Greeks as for friends and kindred, but to conduct himself toward other peoples as though they were plants or animals.” As another example, Euripides in Iphigenia at Aulis wrote a climactic speech where Iphigenia decides to sacrifice herself so that the Greeks can go out and fight the women-stealing barbarian Trojans, explaining,

“Mother, it is the Greeks who must rule the barbarians, not the barbarians the Greeks. They are born to be slaves; we to be free.”

So we can see evidence for an Athenian concept that either some or all non-Greeks were somehow naturally slave-like. Aristotle in his own works references detractors of this view, who instead say that the relationship between slave and master was the same as any other relationship that involved an imbalance of power – that is, that there was no natural characteristic that made a slave a slave. I’m not aware of any attempt by an Athenian writer to construct the kind of elaborate pseudo-scientific theories of race that had shown up in scientific discourse by the Enlightenment, or of any attempt to take the proto-race ideas that did exist in classical Athens and apply them to the selection of slaves. (Perhaps a different contributor can enlighten me!)

I'll update this with sources and some more data in a few hours, sorry.