Sure looks matter. But they aren't much of a big deal. Average looks or even uglyness can be overcome by making yourself awesome.
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still have to go to the effort of picking up girls. As long as I don't have model good looks (which you are either born with or you're not) I won't have girls throwing themselves at me left and right.
Actually, you can. When you get good at this, you will eventually hit a point which I call the "Perfect Storm" - this is when you have made yourself an awesome guy, and have a load of social proof/preselection in a venue. You will literally get girls throwing themselves at you. Now make no mistake, they won't always be the girls you want, which causes all kinds of fun in itself... but it does happen.
But the more important thing here, is that you are upset that you have to be the one to do the initial work with a hot woman. You are moaning about something that defines your masculinity. What are the personality traits associated with masculinity? Confidence, Status, Going after what you want, Boldness, Action in the face of fear, Stepping up. You are moaning that you have to be the one to step up, walk 3 meters to where she is standing, and start a conversation. This isn't something to get upset about, this is something to be happy about. This means that you are the one with the power. You can choose to go after her or not. You have the choice. Whether you want to view that you have the choice - and that you have the responsibility for your own life - as a good thing or a bad thing, is up to you.
I'm sure you're already a good guy. You've probably got a great personality, good friends, etc. But from reading this, I suspect the problem in your dating life at the moment is you are lacking those core masculine traits. Looks don't matter, as they only really make a difference in how many girls approach you. For me, there came a point where my perspective shifted, and I became happy to be shot down 9 times just to hook up with a really hot girl as number 10. It's that resilience, that never giving up, that walking away from every rejection with a grin and a chuckle that gets me with the hottest girl. And honestly, I've never been happier.