So pick a different woman. Acting like women are a monolith and they all are attracted to the exact same guy and nobody else is a crock. Women care a lot less about looks than men do, in general. If you look around in the real world, you'll notice that all sorts of people are paired up, not just the best looking men. But, you mostly have to get off of websites for that to work well, because they are 70-85% men so the few women on there have the supply/demand advantage and the first impression is almost totally physical.

You're right that in a culture where men are largely expected to make the first move, guys probably deal with rejection more often, but as you noted in another comment, taking all of your sense of self from other people's responses is a terrible idea. When you know and own who you are and what you have to offer, the fact that not absolutely every woman is a fit for that is not such a big deal, because you are looking for the person who is a good fit - not just for any warm body with a penis-shaped hole in her body.