I do believe that everyone should simply do what their heart tells them to do!
I'm a very shy person (I actually told the person I like about my feelings for them through text) and the idea of going up to someone irks me, but I understand if someone else feels the same way when approaching their own crushes, be it male, female, whatever. It shouldn't only be 'boys going after girls', but also 'girls going after boys'! It's not like it has never happened though! But it is something that shouldn't be looked at as 'weird' or anything of that nature.
I reckon people feel that boys need to take on a more "dominating appeal", but that's not true! Feelings shouldn't be repressed because one doesn't follow what society tells one to follow! :D