I think I'm going to let my boyfriend be hungry and not feed him enough
That sounds like a punishment. Why won't you feed him?
I'm going to punish him for what he has done to me.
You shouldn't let your bf go hungry over petty things. You should talk to him and let you know how you're feeling.
I have the right to punish him.
Maybe you do have a right to punish him if he has done something bad. But to take away and not feed him food is a bit extreme and might create more problems. I think you should consider a different alternative to punish him, like making him do the laundry for a year or something.