> Women tend to choose jobs that pay less.
This is accurate, but not for the reasons you have given.
Think of it this way. Within a profession, say "lawyer", there are different career paths. One career path involves a lot of travel away from home, and one does not. Because traditionally women are expected to be home for children, women tend to more often select the path that involves staying at home more, which tends to also pay less.
So then, when you look at "lawyer", you see a pay gap, and then you dive in and see that the women have chosen the "lower paying job".
But that still doesn't account for the entire pay gap. It still leaves about 7% difference.
That last 7% is what people are concerned about. That women doing the same job with the same experience get about 7% less on average than men, depending on the field. In some fields (I believe medicine is one), there is no pay gap between women and men with equal experience (although there is still an opportunity gap, where men will be promoted more often with equal qualifications).
Then there is tech, where there is a pay gap between people with equal experience. I've seen this personally first-hand (but at least when the manager was called out on it he made it right and gave the woman a raise, but before being called out, it didn't even occur to him that he was making that decision).
> I have no idea why income HAS TO be distributed equally.
Because people doing the same work should get paid the same for doing it. And because you shouldn't be barred from a career for reasons that aren't related to the job (ie. your gender).
Given that women are 1/2 the population, and given the sample size, women and men should on average be making the same amount of money. But they aren't. And study after study show that the reason is bias against women, and not women's choices.
Don't you think that is something that should be changed?