's post made me actually think a bit and how I, as a "therapies? Bah, humbug" person feel about some of the points, just to shed some more insight. The person close to you might think completely different, of course, but more point of views can't hurt, I guess.
Fear and pride might be a good one, more so than "crazy", at least in my case. I don't care for being labelled crazy, but I would feel like a weak person if I'd have to accept the help of someone who doesn't know me to fix something I should fix myself. If I can't fix my own mental issues, I don't see why anyone else should/could. Fear might play into that, because I would feel at the mercy of some stranger with some fancy degree who hands me a standard fix to get my money. Yes, I'm prejudiced. That, and I distrust doctors.
Medication is out of the question, too, so OJJJEM's right about that one. About homeopathic methods I'd say that probably depends on the person and how much she believes in it.
What came to mind earlier is that if you want to push her gently into the direction, trying to lower the initial bar could work. Something along a first appointment over phone, or maybe even text chat. I would imagine that if I'd get convinced to something like that, I'd feel reassured that I can just hang up or close the chat window after the appointment and never have to think about it again. I don't even have to meet the therapist in person. Awesome. And who knows, maybe the appointment isn't all that bad and I might consider a follow up. You probably get the idea.