It was Diogenes, his disciple, who gave Antisthenes's movement a bad name by snarling at passers-by. They decided that the word must have come from kuon, the Greek for a dog - an early instance of false etymology, because actually it came from the Cynosarges, the building Antisthenes taught in.
Anyway, "cynical" has now become the twin brother of "callous", the popular journalist's word for anyone who has ever murdered a child or mugged a pensioner. There was never any doubt about "callous", which is the adjective from "callus", a bit of hardened skin, and simply means insensitive. But "cynical" has done a smart about-turn. Instead of being a word for people who mistrust the motives of others, which is what it was in ancient Greece, it's now the one we choose for those whose motives we ourselves mistrust.
Again, if it was anyone's fault Diogenes is to blame. In our Renaissance a cynic was an abstainer, a sort of 16th-century Stafford Cripps. But even then people were already beginning to forget Antisthenes and to think of a cynic as a curmudgeon, or just a nasty man, a don't-give-a-damn character. One can see how sooner or later it was going to go the full 360 degrees.
Under "cynical" the Oxford English Dictionary's second (1989) edition had "now esp. disposed to disbelieve in human sincerity or goodness", which, as I say, is the reverse of what the Standard meant by it. But the smart New Oxford Dictionary of English gets it right: "Concerned only with one's own interests."