Baby Ruined Relationship?

To answer some questions: yes, he has always said things admittedly on purpose to hurt people. Doing this to me for the last few years. He initiated sex in the beginning of our relationship but again the last few years he rarely initiates. Twice a year maybe. So I am always the initiator and he isn't tired of being turned down as he doesn't even try in the first place. He's never even tried since baby arrived. He has issues with anger and breaks things when he's mad. Coffee pots, light switches, anything. And over stupid things like getting mad that a button on an electric kettle isn't in the place he thinks it should be, so he couldn't remember how to turn it on and broke the tea kettle. He gets annoyed when I ask for help with the baby 8 out of 10 times. He doesn't wake up at night with the baby. He doesn't help with baby's reflux medications or the 30 minutes of distracting baby after taking them before he can eat. He cooks dinner and sleeps through the night. I take care of baby and work from home too. Oh and he refuses to go to counseling, to go to the doctor for his anxiety, any mental health care at all. And baby was NOT planned. I am apparently very fertile. The amount of support here is unbelievable. Thank you everyone. 💖
My husband is hurtful. We have a 3 month old son who has silent reflux and is very needy. So my sex life with my husband has been non-existent. Our baby sleeps maybe 3 hours at a time on a good night. He sleeps on my chest and I sleep sitting up in bed because no other surface is inclined enough for him to sleep. Yes, I have been sleeping straight up and down for 3 months. No, my husband has not helped. 
Well, my husband read an article online about how babies ruin relationships. He said he was reading his life because we don't have sex and that we will "very likely never have sex again ever." No matter how I told him that it isn't true, that once the baby was better things would change, that we are both tired and stressed from this big life change, he denied it. Then said he should have worked out more, which makes it sound like he's blaming himself but he's really making the assumption that I find him unattractive. 
Whenever he is mad he says these hurtful things to me. He will blame me for the mood he is in (like he woke up grumpy because I didn't get to the baby crying fast enough and that's a "brutal way to wake up"). Later he will apologize and admit he is saying these things ON PURPOSE to put the negative mood on someone else. 
It wasn't until the baby came that I started seeing this as abusive behavior. I would never, ever let him speak to our son that way. So why do I allow it to happen to me?
He is also very demanding of having his way, does not listen to me when I share my ideas (or he will listen but tell me all the reasons why I am wrong). I just don't foresee this relationship lasting forever. I wish I would have seen this before. But then again, our son is my world, and he wouldn't be here without my husband. 
Maybe he is right. Maybe the baby ruined our relationship. But maybe it's because of my husband's behavior and not because of the baby. The baby has just opened my eyes.