I see a lot of disadvantages in having the thought burning bright in my mind that women are not as mathematically able as men (slightly on average and solidly on the right end of the curve), but I don't see advantages. However, I am fairly convinced that that thing is true.

I agree that we don't need to have the thought "burning bright" in our minds. A thought needs to burn bright only if it is very important to keep it in mind while making decisions. But a sober and unflinching look at the evidence seems to indicate that the difference in innate ability (if there is any) is too small to take into account in practically all decisions.