Friend pulling away despite saying how close they feel to me

I (34F) began talking to this guy (31M) at the beginning of this year. He reached out to me on social media and the two of us hit it off and we began chatting pretty much every day after that. He expressed interest in meeting after we realized that we live in the same city.

We continued chatting online and by the spring we had exchanged numbers. We finally met up in June. He suggested an evening walk through a local park and drinks. He seemed kind of nervous but nonetheless, the energy was upbeat and pleasant. Shortly after this he went on vacation for several weeks, but throughout the time he was gone he was, much to my surprise, texting me almost every day.

About a week after he returned I asked him if he wanted to hang out again, and he said yes. It was during this evening that the “touch barrier” was broken by me, with him sort of nervously reciprocating after. Throughout the rest of the evening his body language seemed a little anxious yet still open and inviting, but nothing happened beyond very warm hugs hello and goodbye (both initiated by him).

That was the very end of August. After that the dynamic shifted almost immediately and since then we’ve barely been talking. He’s also become a lot more guarded. He wasn’t exactly an open book before, but now he’s even quieter. I’ve been respecting this and giving him his space. When I asked him if he was up for a hangout last month, he asked for a rain check, saying he’d been extremely burnt out throughout the fall as a result of work stress, but promised that our previously fun dynamic would be rekindled. As of now we’ve not hung out again.

Then a few weeks ago while we were chatting he mentioned feeling “close” to me. I have no clue how this is possible considering we don’t hang out and now barely even speak. He also had previously told me that he struggles to emotionally bond with people, so this closeness he says he feels towards me seems extra strange.

I can’t understand why he’s been so distant if he feels such a close connection with me. I could understand him overstating the strength of our bond if he were getting something from me like hookups in order to keep me around, but he’s not. Plus, he has close friends and a fairly active social life from what I gather, so it’s not like he’s desperate for a friend. Anyone got any insight into what could be going on here?

Something that might be relevant that I have not mentioned is that a close family member of his passed away last year and he’s still working through his grief. I don’t know whether this could be informing his behaviour at all.