Thanks for the replies! I feel somewhat better hearing that I haven't done anything glaringly wrong, and that his story sounds realistic.
You gave your number - excellent flirt move. He lost it - doofus move but hey, it happens. He asked for it agin - good sign! And offered his because, well it'd be weird I think at that point not to offer his. But the ball is still in his court, right where you lobbed it.
Thanks, WillyNilly! That's exactly what I was hoping.
One last thing I will say; I think I've mentioned this before but I was exactly like you when it came to guys - if my friends hadn't intervened I'm sure I'd still be single. One thing that my friends taught me is that although guys will make a lot of effort to 'win' a woman that they are interested in, very few will do it without some encouragement from the woman. How far you are willing to go to show interest is up to you, but I just thought I'd put that out there...
I think this is one of those "romcom" things where men (or sometimes women) go to ridiculous lengths to get to know someone who has, for all the evidence, blown them off. Conventional wisdom may say that men don't hear "no" unless you say so clearly - but those are usually the annoying men you don't want anyway. Nice men hear, "um, maybe," and wonder if that really means, "Not if you were the last man on earth, and if you pursue this further, I'll pepper-spray you."
See, here's the thing - he's made a few self-deprecating remarks that make me think that *he* thinks I wouldn't be into him. So I was trying to figure out how to disabuse him of that notion, without falling all over myself to act keen, know what I mean? Ultimately, I decided to just give the dude my number and let him figure it out. If he's either too insecure, or not keen enough, to take the initiative - then we wouldn't be a good match anyway.
If someone gives me their number on paper I program it into my mobile and then throw the paper away, I think that's what Archie did too.
Yep, that's what he was basically saying he did. Which surprised me, because I'm the sort of person who jams the scrap of paper in my wallet and would certainly never get round to programming it into my mobile, at least until I actually used it. Which he hasn't, yet.
Anyway, thanks to everyone for the helpful advice!