If women know something men don't, we could just ask.

For some knowable things. For others (a) women's self-reported knowledge might be unreliable, (b) women might already be telling men, but this does not get through because men have elaborate justifications for why women's self-reports are unreliable, or (c) the knowledge may be tacit and not easily communicable.

Obviously this applies to any two groups. My guess is that, abstracting from this particular example, most differences between individuals' beliefs is due to a large component of (c.)