I'm going to freak out on a guy at the gym who insulted my socially anxious girlfriend
Why would you want to confront him like that?
He should show some respect to us
I can understand why you are so upset. It's rude for people to insult others, but you should probably handle it another way. You are only going to do the same thing to him, but maybe you should calmly talk to him about what he did.
Talking to him won't do anything. He needs to be taught a lesson.
You can be assertive when you talk to him. Being violent however, will get you banned from the gym.