Any woman worth her salt lets a man pursue her. Not the other way around. If the girl is attractive with an attractive personality-then she has plenty of options and she doesn't need to do any chasing. A man worth his salt will recognize a catch when he sees one and snap her up fast before someone else does.
Its got nothing to do with whether she has "balls" or not. A smart girl will not make it too easy for him as when she does-shes usually left scratching her head wondering where it all went wrong. Guys in general don't trust women who come on to him too strong.