Then he came back asking me to go out for a drink, still reiterating that he didn't want a relationship. I was happy to go along with it in the hopes that he would eventually change his mind and decide he could be with me.
From his point of view: "I was very clear about not wanting a relationship. I consider that this disclaimer supercedes all other info, including perceived "mixed messages" such as if I am very affectionate to her, cuddle her, take her out, tell her I'm falling for her, etc - none of that should be read as meaning I am changing my mind. If DuskTilDawn agrees to date me, she must therefore be cool with this get-out clause."
From your point of view: "He said he didn't want a relationship, yet he treats me like this is developing into something. he says he is falling for me, seems to want to spend more and more time with me, messages every day, etc. Surely he wouldn't do that if he didn't want me to be his girlfriend?"
But what does he want?
Exactly what he's getting - the girlfriend experience. He enjoys your company, likes spending time with you, is (probably) enjoying the emotional intimacy between you and (of course) the sex.
Because you are sleeping with him, right? I know he's nobly agreed to stop the sex if you think you can't handle it and will inevitably fall in love with him. But I reckon that, if you took him up on that offer and removed the sexual element from your dates, he would quickly try to reinstate it. Most likely by ramping up the suggestion of emotional commitment, then letting you both "get carried away in the moment". You would assume he was sleeping with you because he had feelings. He would assume that you were cool with just shagging sometimes.