Person A asks for 90 dollars per year; Person B asks for 100 dollars per year.

Person A does not ask for a rise after one year; Person B asks for 10 dollar rise after one year.

TBH I don't see how it is a company fault.

They are at fault because they are systematically underpaying women of equal qualifications.

It does not matter what the "reason" is. It does not matter if the bias is because equally skilled women merely ask for raises less often.

If for any reason at all, you are systematically underpaying certain groups that are equally qualified and equally productive, you are legally liable and the onus is on you to fix it.

I think that if the person is not asking for more money company has a right to not give him more. Isn't that how capitalism works?

Paying 2 different groups of people that are equally qualified is called illegal discrimination. It doesn't matter what the reason is for the discriminatory pay difference.

It doesn't matter if it is capitalistic to illegal discriminate against certain groups.

So no, they do not have that right, if the result is an illegal pay disparity. The company would be required to correct the pay disparity, even if the reason why the pay disparity exists is solely because 1 group didn't ask for more money.