I don't want to let a girl join my daughter's birthday party
Why leave her out? Why don't you want her at the party?
I just don't like kids that much, and I don't want to be the only adult around a bunch of children.
Your daughter's party is for her, not for you. You should include her friends at the party, whether that's fun for you or not.
It's pretty much just a way for corporate culture to get kids roped in for parents' fat paycheck.
Wouldn't you want to try to have a happier outlook for your daughter? She's the one who's going to enjoy it the most, so why not form it around what she wants? She would love to have all of her friends present!