Am I the asshole for wanting to break up with him after he asked other woman for nudes?

Me and my boyfriend have been together for 2 years. For the past 6 months there have been issues between us and things don’t go well. We work at the same place and our work is pretty hectic. He has always “brought work home” but it hasn’t troubled me since some months ago when it became more of a lifestyle to him and all he talks about is work, he has a second job too to add to the mix. He rarely finds time for me or for our home, he doesn’t clean, doesn’t do the dishes etc anymore and when I ask him to help me he brushes it off and gets annoyed saying he is tired. I get it and know very well how he feels but even a little help would be nice. Due to all of this he hasn’t payed any attention to me anymore, we don’t go to dates, he doesn’t bring me flowers unless it’s my birthday or Women’s Day, no more compliments but instead I get snarky comments etc. All of this has brought us to a place where I feel I want to break things up. Couple of weeks ago I told him about my concerns, we discussed and decided to try and work for our relationship. 2 days later he came home, drunk, yelled at me, argued and kept asking who is the other man. I kept repeating there is no other man, and there really isn’t but he insisted there is someone else. During the argument he messaged one of his friend (a girl) and said that I broke up with him and he regrets not trying a relationship with her. After that he asks her for nudes. She didn’t send any. I didn’t know about this until couple of days ago when I saw the messages. I felt like my heart sunk and someone stabbed me in the back. I didn’t know how to react. How can a man who insists he loves his girlfriend very much do such a thing? When I confronted him he kept saying how he still loves me and doesn’t love her. It was all a game and he wanted to know where the conversation leads to. One thing that haunts me that he said that night is that she has always been the girl who gives her womanly attention

Am I the asshole for wanting to break up with him after he asked other woman for nudes?
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