If people have different gaming styles, then why would they get mad when they clash with another player as if it is the other persons fault?
Human beings are not Vulcans.
When you tell someone you don't want them at the table, whatever the reason, you're still telling them you don't want them. No matter that it seems rational to you, it probably still feels like personal rejection to them. They react accordingly. Pretty standard primate social behavior, really.
I'd be awfully surprised if you told us that you went through a modern school system without having this dynamic made abundantly clear to you. You've been rejected from time to time, right? Weren't you kinda cheesed off, or felt bad about yourself and turned that to feeling spiteful against them? Whether or not you ever acted on that, you know the feeling, no?
So, knowing that feeling, and knowing what just happened, you expect them to feel similarly. Thus, you expect them to be mad at you, you fear they'll talk behind your back.