Women income disparity: Discrimination or Supply/Demand?

Supposedly, women make less than men. Some theories are it is because of discrimination, other theories are because of the choices women make, for example choosing lower paying college majors (art history) or careers (teaching).

Some people think that it can’t be discrimination because:

1) If women truly earned less, then employers would have an incentive to hire them because they are cheaper to hire and

2) Discrimination would be a slam dunk to prove since companies’ salary and hiring practices are under intense scrutiny by EEO watchdogs – the law suits would be off the charts.