If baboons and macaques are monkeys, and if howlermonkeys and spidermonkeys are monkeys, humans MUST be monkeys.
Because they can ONLY both be monkeys if their common ancestor was also a monkey and we share that very same common ancestor. In fact we are closer related to macaques and baboons than to spidermonkeys, which means we share a more recent common ancestor with old world monkeys than both us and the other old world monkeys share with the new world monkeys.
Cladistically, you can not outgrow your ancestry.
Humans are apes, apes are a subgroup of monkeys, monkeys are a subgroub of primates.
Simiiformes is a clear and distinct clade.
There is no such thing for trees, because “tree” is a botanical classification, not a cladistical one.