I want to ask him out but everyone says I should let the man be the aggressor. What should I do?

So I like this guy at a coffee shop I go to. We've been friends for a few months and I've had a crush on him for a while. He's rather shy and soft spoken so I don't know if he likes me or not. My family was always about how the guy should be the aggressor and the girl asking a guy out just comes off as being needy. Is this true? I know I'm not a needy person, I just don't feel like wasting my time hoping he'll ask me out if he isn't interested. Are the opinions on this whole thing based on society's way of thinking or actually based on good facts? Because I have a rather aggressive personality and it's just who I am.