I'm going to get someone kicked out of my exchange trip group
Why would you get someone kicked out of the exchange group.
The person is immensely arrogant and I don't want to hang out with assholes
Trying to get someone kicked out of a group is rude. Others will end up seeing you as the mean person, not the person you want kicked out.
It's his fault that he's being so arrogant. He needs to be shown who's the boss.
While you might not like them, you should not try and get them kicked out. You can just ignore him, he doesn't have to ruin your trip.