Because of biology its very hard for the father to be the primary carer to children after being born.
Until men and women share equal parts of child rearing on average you wont see equal averages in other parts of society like income by age and career choices.
Women have shown a tendency to favor work life balance over income on average which means if you want to increase female mobility in male dominated jobs you need to increase working conditions for men, like equal entitlements for paternity and maternity leave.
Birth rates in western countries are already falling below 2.0 which is a reduction in population.
While some would argue this is a good thing for the environment, the west does not have the majority of the world population and a reduction in population could lead to geo political instability. The majority of the worlds population does not live under democratic rule, a reduction in population in democratic countries only is a troubling trend.