You need to distinguish between the question of what is morally right/wrong and the question of what is generally taken to be right/wrong at some specific time. Slavery was never morally correct but, at most, it was generally taken to be so. (Compare: The earth was never actually the center of the universe, but merely generally taken to be so.)

The first question belongs to philosophy; philosophers try to work out what is morally right/wrong, just/unjust, ethical/unethical. The second question is addressed by many different disciplines: by social historians, as you say, but also by anthropologists, sociologists, economists, psychologists, brain physiologists, evolutionary biologists, and others as well. Philosophers have addressed it in some of these ways -- e.g., Marx within his theory of history and Nietzsche from a psychological perspective in his Genealogy of Morals.

But philosophers also address the second question as philosophers, namely when the analyze changes in prevalent moral conceptions in terms of reasons (rather than mere causes). This sort of effort to understand changes in prevalent moralities as moral progress was especially prominent in the Englightenment. It is less prominent today because, I think, many believe either that it is naive to hold that prevalent moralities change in response to good reasons or that there could not be no good reasons for changing one's moral commitments (just as there could not be good reasons for changing one preferences with regard to ice cream flavors).

I think that both beliefs are questionable. There can be good reasons to revise one's morality -- for instance when it turns out to be incoherent. And such good reasons do sometimes play a role in the change of prevalent moral conceptions. The abolitionist movement and later the civil rights movement in the United States may be good examples. Many people in these movements came to see good reason for revising a morality that was committed both to racism and to equality (to the belief "that all men are created equal, that they are endowed by their Creator with certain unalienable Rights ...").