There are strong historical reasons for this (women are valued for being meek, bashful virgins; men are valued for being aggressive, strong persuers). But it doesn’t change (much) because, regardless of the answer, the woman loses.
In most cases women do not prefer to initiate romantic relationship by direct verbal proposal. As women are more sensitive about rejection. Direct verbal proposal have higher chances of rejection. The another way to start relationship is non-verbal signals that express interest, readiness and wait for acceptance of opposite person. In this way you can easily send your interest by expression of body language and wait for other person signal. Generally nonverbal signals are more attractive for opposite sex.