What is even political correctness? There were always terms considered offensive or not to be used in polite society or even banned - consider laws against blasphemy or cursing. Perhaps PC can be defined as how offense intersects with civil rights movements. Civil rights movements are usually about much, much more things than just language, and offensive language often has nothing to do with civil rights or group prejudice (consider swearing on TV), but perhaps when the two intersects, you can call that PC. Perhaps PC language can be defined as avoiding those subset of offensive terms that are offensive to a minority group specifically.

Probably the most important aspect is the lingistic turn of Continental philosophy - i.e. the growing idea that language generates a form of social reality. Thus changing the way we speak could change social reality - such as oppression. It is not a coincidence at all that intellectuals whom are generally considered focusing a lot on social justice or similar issues can be considered linguistic philosophers - such as Judith Butler or Richard Rorty, who basically invented the very term.

Note that Continental Philosophy and / or Critical Theory has a very, very long history of basically having a, how to put it, anti-oppression or perhaps best put as emancipationist view - it goes right back to the 19th century, such as Marx and even to the 18th, to Immanuel Kant. This is where civil rights angle came from (besides of minority groups themselves focusing on identity more and more and that also matters for language - but then again sometimes the leaders of such communities, such as WEB DuBois have themselves been influenced by the above type of philosophy and social science).

If the question is why did suddenly language matter so much for social justice / civil rights / emancipation, yep, definitely the Linguistic Turn of philosophy.