It has always been the job of the man to make the first move and not that of the lady and here is why;
Society considers it unattractive in women; gender roles in society which we all strongly believe in will not allow the lady to make the first move to approach a guy.
Fear of being rejected; of cos this also applies to the men but a man is more likely to reject a lady who makes a move on him than it is for a lady to reject a man.
Women don't want to look desperate; a man would obviously think that a woman would be desperate to approach him while in the real sense she is not.This stereotype discourages the woman from making the first move.