I find the conventional explanations for sex personality differences, such as evo psych and sex hormone levels might not adequately or fundamentally explain why men and women's personalities differ on average.

The main difference between men and women, if you didn't know already, are that compared to men women are more agreeable (which basically means more nice) and more neurotic (which means they experience emotions more intensely and with more variation). This is only on average of course (I've known women who are laid back or jerks, and men who are neurotic or nice), and the difference is not enormous, but it's large enough that most extremely kind (as well as most depressed) people are women, and most of the most laid-back people (as well as most antisocial people) are men.

Evolution and hormones likely do play a part, but I would posit, and this is just a hypothesis from someone without a formal education, that the main cause of sex personality differences is physical size.

Because men have larger bodies, the density of their peripheral nervous system is lower than that of women. This is why men tend to have a higher pain threshold (which is surprising considering women are the ones that give birth, but that is what scientists now think based on new evidence). I would also argue this is why men are more stoic and women are more emotional. Emotions are largely somatic feelings. You feel happiness, stress, anger, etc in the body in a way that's inseparable from the emotion itself. So it makes sense that the sex with more physical sensitivity is also going to be more emotionally sensitive, and also explains why men handle pain better, and women tend to be pickier eaters and have a better sense and appreciation of smell. (On a side note, I've noticed that people with food sensitivities, allergies and autoimmune disorders tend to be empaths with higher-than-average Neuroticism, and most of these people are female).

People with large, tall bodies tend to be more rationally oriented in my experience. This doesn't mean they're smarter, it just means that they are more comfortable using logic and aren't as swayed by their emotions, because their somatic sensations aren't as intense. If anything it might tend towards slightly lesser intelligence because large people can attain safety and respect with less effort, whereas smaller people have to be better problem solvers to achieve a comparable level of those things. The downside is they tend to be less emotionally sensitive. This doesn't necessarily mean they are selfish or immoral, just that their affective empathy tends to be relatively low because it takes more to make them feel. This can lead them to think sensitive people are "overreacting" when they're stressed, in pain or unhappy.

Having a smaller body I think would also make a person more anxious and fearful, and have a lower self esteem, because they have to physically look up to most people to make eye contact with them (which can cause feelings of inferiority) and equally if not more importantly, most people (especially men) are capable of easily doing them physical harm. Women of course are usually shorter and smaller than men, so it makes sense they are generally more vigilant, yet also be attracted to large men that can protect them (especially if they are confident and protective, but also kind).

I think this is why most crime is committed by men and why women tend to be somewhat less entitled. It's not that men are inherently more corrupt and wicked than women, it's a combination of lower somatic emotional sensitivity (and thus lower affective empathy) and more boldness. Women are also slightly more conscientious than men, one facet of which includes sensitivity to reward and punishment and ability to delay gratification, which I suspect also has to do with their heightened somatic sensations. This is probably why women are less likely to do drugs, commit delinquencies and express their anger physically through violence.

TLDR - I think men and women might have different personality trait patterns at least in large part because men are bigger and women are smaller, making men bolder and less anxious due to lower pain sensitivity and less physical threat to their person, and women more sensitive physically (and also emotionally) due to having denser peripheral nervous systems. Men are attracted to shorter women because they tend to be more sensitive and thus better mothers (this is an extreme generalization), while women are attracted to large, tall men because they tend to be bolder and braver (again, a gross generalization).