They sure love to pitch men against women and vice versa deliberately to silence worker rights movements and they're doing it in more ways than most people are willing to admit. Ask them to close the gender pay gap and a neoliberal will tell you about their women quota and how they placed a woman in a "leading" position (she has no power and didn't get a raise) and how progressive they are already. Ask them for a raise and a neoliberal will tell you how women have it worse than you. You're right in a way of course. It's a convenient diversion for them and nothing more.