I'm thinking of breaking up with my boyfriend because he has anxiety and depression.
Is there a reason why you want to break up with him for having a mental illness?
Not really, I feel he's just being annoying.
That is a terrible reason for you to break up with someone. It is wrong to break up with someone based on their health issues. You should talk to him more about what he is going through and maybe get him some help dealing with it.
I won't listen to you, he is the one who should listen to me.
What you should do is listen to each other; it sounds like he has issues and needs someone to talk to him and support him. If you're not going to be there for him he should find someone who will.