Why can't I leave??????

I wish I had the strength to just up and leave my partner. We have an 8 week old baby together and have been together for almost 3 years but he is so abusive and nasty to me all the time. Every day I am walking on egg shells incase he gets in one of his moods. He has hit and strangled me in the past but hasn't for almost a year now but he speaks to me like shit. He doesn't do anything for the baby nor does he even speak to him unless he's in a mood and not talking to me but then that's just to make a point he is ignoring me. He goes through my phone all the time, if I ever go out (which isn't very often) I have to give him a blow by blow account of what I have done and who I have seen. He has alway been paranoid that I have cheated so I paid £600 and did a lie detector and proves i haven't but he won't even believe that (thinks the lady that took it fancied me so she lied!) I recently found pics of other women on his phone but he still turned it all and me by calling me names, saying I'm crazy and need help. After a week of being really nasty to me he started being nice said he would try and be better and asked for us to work things out.... and then 3 days later it's back to him ignoring me or having a go at me. He is always demanding sex and then gets angry if I'm to tired. My baby boy is 8 weeks and we have had sex at least twice a week since he was 2 weeks old. I know how he is treating me is wrong and I want better for my baby than to think this is ok but every time I finish it he some how twists it so I feel bad for him and take him back. Please can someone pray for me to get the strength to leave him. I am so unhappy and every day my heart hurts more and more because my love isn't enough for him. I just want to be happy with my baby

EDIT.... to the person saying am I the same person saying they will kill there child fucking absolutely not!!!!! That is such an awful thing to say. I want help with prays I am reaching out for surport and guidance. I would never hurt my child!