This is a bit of a red flag.
I suggest you read up on emotional abuse, this is actually a warning sign of a problem.
It’s also a warning sign that he claims to be a survivor of an abusive relationship. This is a common tactic of an abuser, playing the victim. I was just reading about this yesterday and what you are saying is ringing a really really big bell for me.
The fact that you want space doesn’t not make you “a very closed off person”. That is probably a load of bull he is feeding you.
I suggest you google emotional abuse in relationships and read about it.
You should not have to reassure someone constantly. The fact that you are telling him to seek therapy is an obvious sign that you recognize he has a problem.
HIS trust issues are not your responsibility to fix. I remember being young and being in a relationship that sounds just like this one. From the first time we slept together he would FREAK OUT if I wanted to be home alone. In the year we dated he was constantly mistrustful, showed up unexpected and angry at my work and my school, accused me of cheating on him and the few times I was very firm and clear about wanting to be home alone for the night he showed up in the middle of the night CRYING hysterically. I eventually felt so suffocated I wised up and broke up with him. I didn’t even so much as kiss another man til over a year later. 10 years after we broke up I ran into him and we briefly discussed why we hand broken up (he asked). He then said he knew FOR A FACT I had slept with my friend Jim (my weird, gawky, very unattractive art class friend who I would never in a billion years get involved with). Some people... you just neeed to move on from.