I'm not going to invite my friend to my party
Why did you want to avoid inviting your friend?
He impolitely asked if he could bring a friend along and we already had other plans. I don't like that friend.
You shouldn't exclude your friends. It's wrong to do that just because you dislike his friend.
This is his fault.
You couldn't have come to a mutual understanding before this all happened? Excluding him from this seems like a nuclear option you are rushing in to.