Often, people base their identities on comparing themselves to people who are opposite to them. People like to fight enemies because it makes them feel better about themselves. So, some people will twist your words into something they can destroy.

Basically, people like to think that all the evil in the world is in their enemies, and all the good in the world is in themselves.

I highly recommend watching this 2-minute video where John Cleese talks about how extremism makes people feel good about themselves, which kind of relates to what you're talking about: https://www.youtube.com/watch?v=HLNhPMQnWu4