Having a hard time

I haven't posted in awhile. Things have been tough here in our little household. I think Anthony and I may be splitting for good. I love him, I really do, and he claims that he loves me but only sometimes. I found out he was cheating on me, again, only he doesn't consider it cheating. This is what he does: he opens a new email account, emails some girls on Craigslist (I don't really know if they live here or not), and then he chats with them acting like he's going to start a relationship with them. For example, one girl he was chatting with said, "I can't wait to start a family with you." to which he replied, "Me either, baby." He already has a family, with me and Leo. I don't understand why he does it. He says it's just boredom but he won't let me read the rest of the chats. I got into his email account and he changed his password right away. It just makes me think he's hiding something. He claims that if I don't believe him and don't trust him, there's no reason for us to be together. So, I'm heartbroken. Not only that, he just claims that he only loves me sometimes. He says some days he wants to be with me and, others, he doesn't want to be with me and dreads coming home. I get that I can be a nag and a downright bitch sometimes...but I thought the person you loved was supposed to go through that with you. I have no idea what to do. I am so depressed. He doesn't seem to understand why any of this hurts my feelings. He has no idea why I just can't trust him, despite everything he's done. He will not let me see those emails or chats, even though I've told him that's all I want from him. Everyone is telling me to just leave him but I don't even want to do that, even though I probably should. I never wanted to raise a child alone. I always wanted him to have a loving family and I feel like I'm a failure for not providing it to him. That's what hurts the most, that I have failed to give the absolute best possible thing for my son. I can't even afford to live on my own so I don't know what I'm going to do.