I'm A Banana
Potassium-Rich
On the topic of gender differences: Consider height. If you have a hundred men and a hundred women, sampled at random, the average height of the men will be higher. Now, assuming roughly the same population averages as the US, if someone is 5'9", what does that tell you about their gender? Basically nothing. You can't tell male from female by height. But the difference is still there statistically.
But if someone's 5'4", you have a moderately strong suspicion that they're more likely female than male. If you collect enough other data points, even though none of them are absolute proof, you can end up with reasonable certainty.
Same thing tends to happen with personality traits. If you have enough data about a person, you can be moderately confident (though probably not certain) whether they're male or female.
Also, in general, women are quite consistently able to write men convincingly. You can't be a woman in most cultures and not know how men behave and think. It is very easy to be a man in most cultures and be very ignorant of how women behave and think.
It's much more difficult with "personality traits," because personality traits are squishy, hard to define, and vastly context-dependent across populations. Defining something like, I dunno, "Politeness" is fraught with pitfalls and vaguenesses that defining something like "height" is free of. It's not as easily measurable.
And I do imagine, in general, it's hard to be a woman in most societies without having to be concerned with what men think on some level, simply because men are the gatekeepers to power and prestige in most societies. If you want those things, you have to figure out how men are going to see you. Which, I bet, sucks sometimes.