I asked for a divorce, unsure if I should move forward with it? (30F, 30M)

I am longing for my husbands change to be permanent, but feel like it is fake.

For context, my husband and I have been together for 5 years. We have 1 child together. He is an avid gamer and throughout our relationship his lack of household chores, and overall just being a good partner have gotten worse. Any sort of emotions or feelings I have, would be met with an eye roll, huff and puff, and told I'm over-exaggerating or that "I start all of the arguments, if it wasn't for you starting them, we would never argue." Being told I constantly ruin his nights when it was date night and I'd ask him to get off of the computer with all of his friends in voice chat, and all of our arguements would end in him screaming at me (yes screaming.) He has never contributed to household responsibilites, and would instead ask me to make him "a list." I would make the list, and he still would not do half of the things on the list. Throughout my pregnancy I would work full time, and still come home and take care of the house (he is a student so he is home majority of the day.) For YEARS I begged for change in our romantic life, his contribution as a person who lives in our household, and overall just the way he treats me. It would change for 2 days, then go back to normal.

When we would argue, he would degrade me with name calling (typical bitch,cunt, etc) but always escalated that he wanted a divorce, he doesn't love me, and is only with me for our child. Our last arguemnt ended with him telling me to k*ll myself.

That next week, I had such a realization of the way he was treating me - I told him I wanted to seperate, and I also wanted a divorce. I was met with him basically not believing me, he would sleep on the couch and say "were not together so he won't share a bed with me." I'm unsure when it actually clicked for him that I was serious, and that after he completes his degree in the Spring (he is my source of child care and kicking him out would not be fair since we agreed on this long degree together) that we will go our seperate ways and I will file for divorce.

Since he has come to the realization, he cleans the house the entire day. He has cooked dinner for me twice a week (he's NEVER cooked me dinner) and hasn't really touched his computer. This has been roughly 2 weeks. Unfortunately, on Halloween, he told me he had been going to therapy for his anger and just the way he lashes out. Long story short, I found out this was a lie. He had inquired, but had never done a session with a therapist. He claimed he had been going for 3 weeks. When I asked him about it about 5 days later, he tried to further his lie, until I told him to just give it up, in which, he did - and admitted he was lying.

I feel like this just put us back at square one. I feel angry by all of his contributions and feel bad about being angry (dumb I know.) I'm so angry that I begged for this for years and was met with nothing but disappointment, and only now that I've checked out - does he care. I can't help but feel like he is doing this out of fear, and not out of actually WANTING to change (considering he lied about going to therapy and just never did.) He assures me he has thought long and hard about our relationship, and is in love with me and is willing to fix anything and do anything to prove it to me. Clearly I love this person I've stayed this long in this relationship, but I can't help but feel like it was/is abusive and he is just changing things so I take him back and eventually it will all return to normal. I feel a constant confusion of what my reality is since for years I was told that I'M the problem, that I'm insecure and an awful person when in actuality I would just be asking for him to spend time with me or help me clean the house/cook meals. I feel like I am just not level-headed in this situation any more.

Any advice is appreciated.