Do I stay orrrr

We have been dating a few months and as we are getting to know each other, it seems like I’m finding out more and more about his mental health.. he has ptsd and some type of mood swings. I’m not the type it person to just walk away from someone that has struggles like that because I too suffer extreme anxiety and depression. But every time something upsets him (which seems to be very often) he responds with “I’ll leave you alone” or “I’m just a bad person I’m a failure, I’ll leave and you won’t have to worry about me”. I always reassure him I care about it and I don’t want him to leave but I can only keep doing this so much. Is it wrong of me to think I need to be with someone a little more mentally stable? Like I really care about this guy but I can’t have him slamming doors, throwing my flowers away that he got me just cause we have a disagreement..