Ok, I did a little (more like googled and read a few dating articles and forums) research. What struck me is there are a fair number of girls that do approach guys. Personally I don't approach guys because back when I was single I didn't have the confidence to. Yeah, girls have issues with shyness and lack of confidence. And for that reason until I was 25, lost weight, and became more outgoing I never got asked out.

Girls can be as shy as guys, and won't approach them because they don't want to be rejected. Some girls who approach guys get rejected because the guy sees it as meaning she's easy, or controlling and doesn't want to deal with a girl like that. But probably the biggest reason is girls are less interested in a guy's looks and more interested in personality. For me it's hard to tell if a guy is a good guy or an asshole just by looking at him. I don't want to go up to a guy because I think he's cute and then find out he's an utter jerk that I don't want to share air space with.

But I think the reason you don't get asked out is because you're sending out negative signals. One thing I've learned since I started dating is even though I was very socially inactive when I was younger I can tell when a guy is interested in me. It's intuition, for some reason I just know. Women are very good at reading signs. We can easily tell what the guy is thinking because of body language and facial expression. It's like having sensitive hearing, we can hear well, but guys are practically deaf. In order to get a guy's attention a girl will have to practially scream before a guy will get a clue. My point is that you may be picking up on the signals, but you may be sending out your own. You feel very hostile about approaching girls, and you probably convey this whenever someone shows interest in you.

There are probably girls out there that would be thinking about approaching you. They could be looking at you, seeing if you are interesting trying to figure out what kind of person you are, and thinking about coming up and talking to you. Once you notice this instead of smiling at them, you frown wrinkle your forehead, turn your body away, etc. This shouts at her "leave me the fuck alone!" The message is loud and clear and they aren't going to bother with trying to talk to you.

You could try being more assertive and asking girls out, but there are other ways you can improve your chances as well. You do have to get rid of the hostility because you will drive girls away without even saying a word. If you are giving hostile signals you're already telling a girl no before she even gets a chance to talk to you. You have to be open to girls approaching you. Secondly, you could try the internet or joining a club or something where you could make friends with girls. This helps you with getting more comfortable around girls. Your best chances of being approached is becoming friends first and letting her know what you are like. Once a girl gets comfortable with you and figures out you are a decent person your more likely to get asked out. Hope this is helpful.