Here's my 2 cents on this gender inequality problem.
Generally there's a split because women and men have different interests. If you like something that another gender is going for, sure go ahead and try for it. HOWEVER.
Many of these jobs are gender unequal not because of less opportunity but because men and women are just not capable most of the time in certain position. Take construction and heavy industry. It's dominated by men because a lot of the time you are required to lift heavy materials lots of the day, manhandle equipment and machinery around, etc. Not many women are physically capable of that. Sure some are and they are completely happy in what they do and can keep up no problem. Just one example but there are lots of other jobs that are the exact opposite. Men just most of the time aren't suited for them.
Now about that pay gap issue. Yes there are tons of stats reported all the time. The problem here is that's all that's reported. Just the pay difference vs hours worked. Nothing is ever said about part time vs full time. Experience in the field. Knowledge of said field in certain capacities, Overall hours, etc. Why should a women get paid the same as a man in the same one when he's been there several years and she is just starting out. FACT. She shouldn't. Same goes the other way around. YET we don't ever hear of that. All we ever hear are of the "Pay gap". No actual facts that are crucial to the stats are shown. You know why? Cause they are trying to spin a story and make a big deal about something.
Thoughts here aren't quite finished but i think you get the idea