I think the main issue with using "but" everywhere is that the context is typically wrong. Starting a sentence with the word "but" without there being anything to follow up makes you sound like you're trying to prove something wrong, without there actually being such a thing present in the conversation to begin with. Sentences such as "Everyone but Jack arrived today.", or "I like these shoes, but they're a bit too tight." are grammatically correct uses. I personally despise its usage as a way to follow up what another person said, though. It feels intrusive and annoying, it almost makes it sound like the person themselves was trying to use that word in the first place, as if to suggest "Surely, this is what you would say".