I think that you're right to assume that it's unlikely to be coincidence, but framing it as "something wrong with you" is neither accurate nor helpful.

I expect the "assuming I'm happily single" thing is probably a big factor. More generally, I think people make the division into "potential romantic partner" and "not a potential romantic partner" very early on in their acquaintenceship with someone, usually long before they know enough about one another to see whether a relationship would work, so to some extent the trick is getting into the first box more often. I find that flirting a lot helps!

Also, and this might help with the last question as well, pursuing casual things, before you've made a significant emotional investment, can open the field somewhat, and allow you to feel more relaxed about the whole thing when you find there's someone you're interested in quite seriously.