Point the second - Hypothetically, if this:

the difference in average pay between women and men is mostly attributable to differences in ambition and time voluntarily spent at home with children.

is true, then gender pay inequities do have an innocuous explanation- namely, the above. Kaj_Sotala made no claims beyond that, certainly not to the extent of claiming the above statement is true in the real world.

Hypothetically, I agree with you.

I think this might be confusing pedanterrific because if I read you right above you don't agree with him. I thought your position was similar to the one I made here that that explanation of pay inequality, even if true, is not innocuous because the reason why men and women make different choices about work and home life could be harmful social pressure, or some other reason that we don't think people should have to face in an ideal world. But I could have misread you when you wrote this:

I don't think I'd use the word innocuous with the example of this reason for this gender difference. If it is a rational choice, why don't both genders make similar choices?