I've always been under the impression that if a person has a bit of interest they'll make time for you.
If someone's working a million hours a week, around the clock, there is literally no time to make. Have you never been in those shoes in a full-time job, working 70+ hours/week, overnight, on call, sleep- and food-deprived, etc? I'm not in medicine, but this type of schedule is common in the USA in many jobs.
Is it really impossible to meet up like he says, or is he just not interested?
This is illogical in light of:
- "I 'liked' somebody's profile, he liked mine back."
- "He always responded immediately to my messages,"
- "I told him I would like to meet up at some point and he said he would like that."
- "I gave him my number and he texted immediately."
- "I asked him if he wanted to get together this weekend and he said 'I'd love to....' "
Sure, of course anything is possible, and the guy's not interested. A guy who's truly not interested wouldn't behave like that and play mind games in order to lead you on. In your short post alone, you've given multiple examples where he has demonstrated behavior indicating interest through both his words and his actions. And has been forthright that his short-term schedule is prohibitive with introducing new people in his personal life, which is likely non-existent.
I would be more patient, empathetic, and not worry so much. This worrying and insecurity could turn into a self-fulfilling prophecy where you end up nagging/clinging/smothering, and he truly goes from liking you to being annoyed with you to the point of running away.
That's just my impression based off the information you've given, and it's just my one cent.
But what is the point of being on a dating site if you don't plan on meeting people?
I guess I got asked that question years ago on OKCupid, so I ended up just disabling my account (best decision ever). You have a point. I dunno. Maybe his heart desires companionship (we're all human), but life circumstances simply don't allow it.
Or maybe he's trying to avoid confrontation and doesn't like you but is just being friendly. Which doesn't make sense considering he said he'd love to meet up. A guy who wants to let a girl down gently wouldn't say stuff like that. At least I wouldn't.
I recommend giving him the space he needs and not pestering him too much, but a few times a week send classy, sexy pics to him without comment, forcing him to become overwhelmed with desire.
Kidding.
And honestly, I just read your post again. You asked if he'd like to "get together this weekend." Well schedules book fast, so maybe it's way too short notice. He said "I'd love to, but...." Since he seems to have the busier schedule, why not put the ball in his court and have him suggest a good day/time in the future to meet? You say, "He didn't offer any alternative date we could eventually meet," but maybe you weren't direct enough and simply assumed he'd offer an alternative date.
Good luck. And welcome to SDN!