I thought it was established in Chamber of Secrets that Mudblood was the worst thing you could call a Muggle-born witch or wizard...?

Actually, you know what? Let's not even have this conversation. Suffice to say there are people out there who refuse to admit Snape has ever done anything wrong and try to make excuses for his bad behavior, even if it means victim-blaming the shit out of the other characters. They make my skin crawl, and not in a good way. Makes me feel sorry for sane Snape fans.

I certainly don't think that Snape's behaviour towards his students has anything whatever to do with concern about their progress; I think he likes to make other people feel worse in order to make himself feel better.

Exactly! Which was, last time I checked, the very definition of a bully. But try telling the Slytherin apologists that.