why shouldn't adults bully each other?

[Esquilax]

people contradict. i know that morals are subjective, but they don't really exist.

There's no grand, overarching Morality with a capital M, I agree. But that's not the end of the conversation: there might not be a set of rules embedded in the universe, but we are real entities existing in a universe that has constants that we can observe. Life is preferable to death, pleasure is preferable to pain, freedom is preferable to slavery; these are just objective facts, and we can use those to construct a fairly complex system of morality, even if the finer details of it vary from person to person.

So no, it doesn't "matter" whether adults do or do not bully each other... but I bet there's a human community that might frown on it anyway.