The ego thing is bigger than just getting over the possibility of rejection. Not only do you have to not care what the girl thinks of you, but you also have to not care what her friends or other onlookers think of you, and you also have to not care too much what the outcome is.
You have to want the outcome enough to go and get it, yet if you display that you're desperate for the outcome, you probably won't get it. And if you're desperate for the outcome but pretend that you're not in order to try to trick her, then there's a good chance that she'll see through your trickery.
If, like me, you've been terrified much of your life of displaying interest in a girl, it can take a while to get rid of these old fears.
You have to want the outcome enough to go and get it, yet if you display that you're desperate for the outcome, you probably won't get it. And if you're desperate for the outcome but pretend that you're not in order to try to trick her, then there's a good chance that she'll see through your trickery.
If, like me, you've been terrified much of your life of displaying interest in a girl, it can take a while to get rid of these old fears.