> It's pretty common to make sweeping generalizations in casual conversation, which this is
It's interesting that you chose the term "sweeping generalization". It almost always carries a negative connotation. In fact, it's considered to be a logical fallacy (see https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFalla...).
> I find it really annoying when someone says something like "everyone likes cats!" and then someone, inevitably, will hop in and reply with "ACTUALLY, I hate cats."
I'm sorry I annoyed you. I find it annoying when someone speaks for me and gets my opinion wrong.
edit: Is it really "inevitable" though? It happens every single time? (just kidding)
> This isn't a mathematics proof.
No, but communicating clearly and honestly is important, even in casual conversations.