Hello. It sounds like you have two totally different issues going on here. Your main question of should man be the one to initiate going out, that completely depends on the two people involved. There are no 'rules' to these types of things. It also depends on your culture and how you were raised. I believe that it should be 50/50.
As far as the other issue about him being an alcoholic and not enjoying your company, that sounds like the relationship you are in is not a good one, or at least not a healthy one. You should never be afraid to say what you feel and it sounds to me like your relationship is not going anywhere positive right now. He is blaming you for things, you are obviously not happy with him, he doesn't seem happy with you, etc. Is this who you want to be with?