If you were having, say, a birthday party, and you invited the children, but the parent wanted to bring the child's siblings or another tag-along friend, wouldn't it annoy you?
It would really piss me off if someone bought another child who wasn't invited with them, because my kid (unless they somehow were friends or knew each other) would barely know them and I'd think that it wouldn't be fair on said child because they wouldn't know the person whose party it is.
Probably gets worse when the uninvited ones expect party bags and food.