He says he isn't looking for a relationship but...?

We started out as a kind of casual friends with benefits thing, and neither of us was looking for a relationship. But things got more serious and it transitioned to the point where we both agreed that we were dating - but not in a relationship.
Sex is not a big part of it. We both admitted that it's more of an emotional connection than anything else. He once told me that we had great chemistry and compatibility, and that he really enjoys spending time with me.

Recently he keeps wondering out loud about how this will all end. I'm not sure how to take that. We had an original implicit 'agreement' that this would end when I went home for the summer. But plans changed and I ended up sticking around. So we're still seeing each other and spending weekends together.

Things have been going great. He even suggested that we start seeing each other on an almost daily basis.
But there's always the implication that he still doesn't want a relationship - and I'm beginning to want one. For the life of me I can't begin to understand him. He said he doesn't want a relationship, but then sometimes backtracks and says that it's not completely out of the question. And then he acts almost like I am his girlfriend - asking me along to his colleagues' dinner parties, all the romantic hand-holding and cuddling, moving his schedule around to spend more time with me, even helping out with housework etc. And he cares about me, actually cares. When I walk out at night alone or accidentally cut myself he gets all worried about me.
It's frustrating because I don't know what he wants, and I don't think he does either.

What's his deal?

have you asked him straight up? and if he doesnt give you the answers your hoping for you should respect yourself enough to walk away.

honestly i think if he really wanted you-you would have been his gf from the start. i dont understand why people settle for this FWB bollox.. its obviously not working for you and i am yet to see a success story that started this way.

way too complicated for me. and i wouldnt allow a man to treat my like a toy that he can pick up and drop when it suits him.

not wanting a relationship just means he dont want one with you. dont be surprised if he has no prob committing to the next girl when she refused to let him f**k her without exclusivity. to gain his respect-thats normally all you gotta do. set those standards higher or else all you will ever be is his "for noe" girl

id give an ultimatum "all or nothing" and if hes still confused walk away

sounds to me like he wants the benefits of being in a relationship without exactly having the formal definitive title, maybe something to fall back on if he slips up? if you really want to have a relationship or find out where you stand, sit him down and find out whats on his mind.