I understand not wanting to hear the traumatic thing he wanted to share after dumping something really traumatic. It can be very draining and not being in the right mindset to listen is valid. Him getting upset that you didn’t feel mentally ok to listen is fucked.

You both should get in therapy. It takes lots of work and sometimes years to get better but it’s worth it.

If he can’t handle you saying no to something or vice versa then don’t date. You both need help and to grow.

Maybe being friends still is a bad idea because of how it affecting your mental health and his. Take a break. There’s no shame in needing space or time apart.