That he's frustrated with you for not sharing, suggests that he might have more to gain from your sharing than you would. As it happens, I seem to have missed pretty much everything you've posted about this group so I know nothing about them. Accordingly, I'm simply going to let my imagination run riot:

• For whatever reason, he has doubts about his own trustworthiness and wants you to reassure him by trusting him.

• He once did something in group that wasn't OK with him; he's not entirely satisfied that he's cleaned it up and won't do it again; he wants you to bail him out by proving you trust him; and he's frustrated that you aren't playing along.

• He's not ready to forgive himself so he's hoping you'll forgive him so that he won't have to.

• He secretly resents you for some reason and has been yearning to flame you in group, but so far you've been careful not to give him any ammunition.

• He hasn't anything against you personally but is just seeking to show off his flaming skills against anyone who'll give him the opportunity.

• He's looking for someone to rescue in order to take his attention off his own issues, but you're not volunteering to be rescued nor even telling him what you might need to be rescued from.

• He thinks he'd feel less embarrassed talking about his stuff in group, if you talked about your embarrassing stuff first. Come on, don't keep the poor guy waiting!

• He wants to impress you and put you in his debt by knowing stuff about you that he hasn't used against you in any way -- so that when he does spill something embarrassing about himself, he'll have something to hold over you in case you blab, or make fun of him, or whatever.

• You have to prove you trust him first; then (he thinks) he'll feel ready to try trusting you.

As I see it, you don't need to know "how". Trust is something that happens naturally when you let go of your inclination to distrust. If you see a risk of being "burned" and you're not willing to be burned, distrust sounds to me like an entirely appropriate response.

I'd say what you need to work on is not trusting per se, but identifying what the risks are for you and watching yourself choose to accept them or not. It's not a bit better to trust and regret trusting, than it is to distrust and regret distrusting. You can, however, go into a situation with your eyes open, choose either to trust or to distrust, and be equally satisfied with your choice either way irrespective of how the situation eventually turns out.
I'd think that simply experiencing this experience and owning it as yours will be worth more to you in the long run than any form of "conquering" it. Good luck, MUE!
(!)