He's an alcoholic, so why assume he has any rational thoughts or emotions in any form right now? My dad was an alcoholic and was in AA for years and he used to always say something to me that made sense. "You can't talk sense to a psycho." It's sounds like you're trying to make rational sense from behaviors that make no sense. He doesn't have the mental or emotional capacity to be in any way unselfish enough to be in a caring relationship right now. He doesn't even care about himself.
It is possible that he does love you! I was in a relationship with my ex for close to 5 years, in later years I found out he had been cheating pretty much the whole time. I hated him so much for putting me through so much pain (There was a lot more bad points in that relationship to) I came to realize though that he did actually love me but some men want there cake and to be able to eat it to (I am not trying to make excuse for their actions because I do not agree with cheating at all)
But to be honest with you, your relationship is poison, you deserve to be happy. It's hard to walk away but you will thank yourself in the long run.
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