Because a peeve is like an itch that you just have to scratch….
Exactly like, in this case.
Itch, the noun, is a physical sensation:
Starched clothing against the skin can cause an annoying itch.
Itch, the verb, is the act of feeling that sensation:
Joe’s skin itches where his starched collar rubs against his neck.
The verb for what the starched collar is doing against Joe’s skin, on the other hand, is scratch:
Joe’s starched collar scratches the skin of his neck.
Scratch is also the verb for what Joe does to relieve the annoyance:
Joe scratches the itch caused by the starched collar rubbing against his skin.
The starched collar, on the other hand, does not itch Joe’s skin. It scratches it. Which makes it itch. Which makes Joe scratch it.
Get it? Good.