I'm going to make someone leave the gym today
Why do you want to do that?
He's been getting on my nerves and I think my girlfriend will be happier if I am able to keep him away from her.
Attempting to get someone to leave the gym that they're a member of is rude and inappropriate behavior. You should try to be kind and understanding whenever possible. If the person is annoying you and your girlfriend try to talk with him rather than try to antagonize him into leaving the gym.
I'm not so sure. I think maybe a good fight will get him to go away.
If he's truly bothering your girlfriend that much, she should take this person aside and respectfully tell him he's interfering with her workout. If he persists, she should complain to management. Violence is uncalled for except in cases of self-defense when no other options are available.