She's not really wrong to be afraid. If she's risk averse it isn't a "steady" form or income compared to a lot of other jobs. It's also something that people seem to have complete control over, give the whole "it's a skill game" spiel, and then six months later come back with "sick, sick downswing, I'm busto!!!!! what do i do!!!???" all the time. Actually, I think the way you're talking to her about it in that respect is pretty wrong. If you're going to do the whole "it isn't gambling" spiel I think you've got to accept the reality of the situation a little more yourself (and yes, I consider myself a professional gambler and am saying that).
Basically, if she isn't comfortable with it, especially if it's against her value system (and just skimming your o.p. it seems to be), you're probably not going to change that about her and probably shouldn't want to. Poker relationships fail all the time even when both parties are comfortable with that part of the situation. In your case where she isn't you're drawing damn near dead imo.
Also, most women are going to be pissed/give you some grief over ditching them for dinner. Learning how to not turn that into a drawn out argument might be a more important skill than debating the merits of poker. "Sorry, you're right...yeah I should be somewhere when I tell you I'm going to be there. Sure thing. etc." might have been the much more shark play there. Actually, I'd bet that's more central to any problems than the poker thing unless you're getting into "put a ring on it" territory. There's nothing that says you have to beat your gf at debate club every time she gets pissed.
Being in your 15th or so year of school and not being able to spell guarantee might also be dampening her long term hopes for the future if the poker thing doesn't work out, can't blame a girl for that...