My gut told me there was more going on here than just plain old jealousy and he's just proved me right - unfortunately.
our life is boring in comparison, so yet again it's YOUR fault he did this because YOU made him feel that way by not making enough of an effort in the relationship 
IF that were true - why hasn't he said or done anything about it in the 4 years you've been together? It's a blatant lie to shift the blame back on to you.
He feels like he is comparing himself to to ex all the time Oh yea, sure! His head is so far up his backside i doubt very much he feels inferior to your ex. Also -remember he KNOWS your ex cheated on you, so there is NO WAY he is 'comparing' himself to ex and feeling like he's coming up short. Load of bollocks!
I don't think he actually has a high opinion of you let alone have any respect for you. He's talking to you and treating you as though your head buttons up at the back! His mask is slipping a lot quicker than he realises.
he didn't know why he had done it, yes he does. He KNEW you weren't up to anything but he CHOSE to do it because he is mentally obsessed about you having had a life before you met him. He is hell bent on wiping all trace of your ex out of your life so he's going to keep on creating issues about that until you do.
I mentioned therapy and he said he didn't think that was necessary and that he knew he'd done something stupid and untrustworthy but he didn't need to speak to someone.
It wasn't 'stupid' - that's minimising it. He lied, stole and broke your trust - deliberately and knowingly.
He NEEDS therapy. He's been obsessed with your ex for FOUR YEARS. That's four years of - slagging him off constantly, expecting YOU to slag him off, of publicly humiliating YOU to get his own way and of manipulating you and making you watch every word you say. Obsession is not logical or rational, it doesn't 'make sense', what it does is enable you to do things you wouldn't do if you were thinking rationally. He hasn't been thinking or behaving in a rational, logical manner where your ex is concerned for FOUR YEARS!
And now he's refusing to discuss it with you or even formulate his own plans to deal with it. He's just giving you empty promises which he doesn't even believe himself. he KNOWS he is going to keep on doing shit like this until he gets his own way. And until he gets his own way he's going to lay ALL the blame on you in a passive aggressive way, so no matter what you do to protect yourself and your dc - you will always be the 'bad guy'. When you leave him he will tell people YOU didn't make any effort in the relationship, that YOU put everyone else first except him, that YOU made him feel like shit, that YOU couldn't be trusted hence why he 'had' to 'check up' on you, that YOU threw him out because YOU didn't love him.
Whether you choose to stay or go in his mind it will always be YOUR fault. I seriously feel he has some deep underlying mental health issues that he is denial over. Going off what you describe, he sounds like he has some narcissistic traits as well. i have a family member who exhibits ALL the traits of a narcissist, i believe she actually has full blown NPD. They not only lack empathy and play shitty games like this, but they create an alternative reality in their head and then actually believe their version is the ONLY truth. Any problem or issue they have is ALWAYS somebody elses fault. They cannot apologise sincerely, they give backhanded apologies that mean nothing, acknowledge nothing and absolve them of all responsibility. Unfortunately you cannot 'win' with a narcissist, you either accept them as they are or you keep them out of your life.