When men pull away but seem annoyed when you don’t chase. What do I do?

TLDR: He tells me to leave him alone, blocks me, says he's done — then seems annoyed when I don't reach out, like it proves I don't care. He also says he wants "actions not words" from me but won't say what that actually means.

I’m 27F he’s 32M, after a few months together broke it off with me. We’ve been going back and forth for the last few weeks about who did what wrong, issues we may have (which are unrelated to the relationship and more past experiences) and a lot has been realised. One thing I keep getting stuck on: he'll tell me to leave him alone, block me, say he's done — then a day or two later he's annoyed or hurt that I haven't reached out, like it confirms to him that I don't actually care or wasn't trying. Therefore I keep trying to work on this to prove I do care and do want him.

I feel caught either way. If I reach out after being told to back off, I look like I'm not respecting his space. If I don't, it seems to prove whatever assumption he already had about me (that I don't care, wasn't invested, etc.), even though that's not true.

He's also said a few times that he wants to see "actions, not just words" from me, but when I ask what that actually looks like in practice, I don't get a clear answer. I genuinely don't know what he means by it, or what he'd actually consider proof versus just more talk.

Genuinely asking for a male perspective here. And when a guy says he wants "actions" but won't specify what, is there usually something concrete behind that, or is it more just a vague way of saying he's not convinced by anything at this point?

He says he’s done and no longer interested, too little too late, but over these last few weeks he’s still asked how my day has been and had civil/friendly conversation here and there. In the beginning he was very certain of me, assured me of no one else, mentioned living together. And now it’s just me that wants to make this work, learn and grow from this together.