What comes first, non sexual intimacy or improving sex life?

I (40f) have been going in circles with my boyfriend (40m) about this argument around our sex life and I feel like I'm losing my mind. We have been together for about 3 years. He says the problem in our relationship is that we only have sex about once every 2 weeks, (though it's often more than that but he doesn't count oral) and that it makes his life hell.

The main issue to me is that he is in such an insufferable mood all the time, "screaming and cussing at the top of his lungs over spilling a drink" kind of anger. He complains about sex having to be scheduled around kids sleeping or being away when that seems normal to me? He's pissed off if I want to go do something with him when all he wants to do on his days off is relax and nap. The absolute worst part imo is that when it all of this compounds and puts me into a crappy mood, I can't bring it up to him or he will explode about how maybe if he was having sex as much as he used to he wouldn't be so shitty.

I've tried to explain that I need emotional intimacy throughout the day, touching me in non-sexual ways, asking how my day was, spending time together, not staring at his phone when we're together etc, but it always turns into an argument with reasons why I am not good enough and never taking things into consideration.

Lately he's been casually hunting about "looking elsewhere" and how he had more sex when he was single, like I am ruining this relationship. His exact words were "I dont act like a boyfriend unless I get boyfriend benefits. Otherwise your just a friend or something." I apparently "hate sex". He feels like I'm making him into this person by not having sex with him enough. But I also want a healthy sex life, all I'm asking is for basic respect. I'm not trying to use refusal of sex to get him to do what I want, I just am not attracted to him when he's been rude and dismissive. It actually makes me feel really depressed and I find myself losing interest in a lot of things.

TLDR when your sex life is dwindling, what comes first, the sex life or the respect? Should I just try to "put out" more and will it make him start treating me better?