Dohwa did it so he could forget everything. We know by now that once someone dies in the tails, he/she loses her memories and his/her consciousness. He now knows he somehow put Juda in that situation because that should have been him. And knowing everything his family did to Juda's family, he feels like he doesn't have the right to love her because he felt so guilty. His pain comes from knowing everything, knowing he can't do anything and being guilty of it. It's too much to bear. Thus, he chose to just forget everything. It's not that he wanted to die per se, but he wanted to forget everything. I still prefer the Dohwa in the webtoon though, for his innocence and depth that led him to make that drastic decision. It was just too hard for him.