When I was young, not knowing who Jane Goodall was, I was dragged into lunch by event planner who showed her around Beijing, and wondered why this lady was talking about chimpanzees so much. This was the year the Nokia released Snake, I remember getting enamoured/distracted by her monkey talk and lost a near perfect snake run.
Monkeys are just the simiiformes minus the apes. That's just a paraphyly, which is totally fine.
If you don't like paraphyletic labels for aesthetic reasons, just include the apes to make it monophyletic. The main reason we don't is that many people have strong, visceral reactions to being called a monkey.
You can't do that to fish or trees without including a bunch of things that are obviously not trees and fish.
"If it doesn't have a tail it's not a monkey, even if it has a monkey-kind-of shape. It if doesn't have a tail it's not a monkey; if it doesn't have a tail it's not a monkey: it's an ape."
