The main problem is not that women who work the same jobs as men get less for it.

Then they should improve their negotiation skills. It really isn't difficult to find out what is the market rate for the position and then based on your experience and other variables determine a salary you're comfortable accepting as a minimum.

Women are not given the same opportunities as men - i.e. they don't advance up the ladder as quickly as men

Bullshit! Women in India and other Asian countries are going into STEM subjects because they need to do so to earn a livelihood. The women in the west choose not to do this by majority, because they live a life of comfort with horses provided by daddy, and not a life of squalor whereby they're likely to drop their bowel movement in the middle of the road for eating some seriously dodgy street food. They choose not to do those things because they're in a much more comfortable position and don't need to do those things. Their interests and priorities lie elsewhere. Are you seriously going to tell me that women in the west don't have the same opportunities as women in India?