Man is m’chuyiv in p’ru u’rvu, not the woman. But a man can’t just go around procreating. However, kiddushin is a matir for the act; hence he is obligated to marry as a hecha timtza to procreate.
The woman, however, is not m’chuyiv in procreating so there is no obligation of marriage; but she has the option of kiddushin if she wants children and companionship.