Actually, women do ask for more pay
Studies show that women are more likely than men to negotiate their job – which often results in higher pay.

Summary:
• Women still earn significantly less than men, particularly at senior levels, despite being increasingly more likely than men to negotiate their salary.
• People (both men and women) who claim (erroneously) that the gender pay gap is caused by women’s reluctance to negotiate, are more likely to oppose policies that could actually reduce it.