Regarding "men tend to have more variance in everything due to having only one X chromosome": So, there are lots of recessive genetic conditions: for a particular gene, if you have two copies of the common A allele, you're normal; if you have one copy of A and one of the rare lowercase "a"—written as Aa—then you're normal; but if you have "aa", then you have the rare genetic condition.
Then, if we suppose that 99% of people's copies of the gene are A and 1% are a, and that there's totally random distribution, then you can calculate that 98.01% of the population has AA, 1.98% has Aa, and 0.01% has aa. Which means 99.99% will appear "normal" and 0.01% will exhibit the condition.
Now, what happens when the gene is on the X chromosome? Women will have two copies, men have one. What happens when a man has "A" or has "a"?
I think the mechanism for recessive genes is often something like, "Allele A codes for an enzyme/protein, while allele "a" codes for a version of it that does nothing; if your body is producing the normal amount of that enzyme or half of it, it still has the normal result, but if you produce no working copies of that enzyme, then you get the unusual result." Or something like it. So in that case, a man who has "A" will appear normal, and a man with "a" will have the condition.
The result would be that, for an "X-linked" condition, 99.99% of women will appear "normal" (1.98% of which will be "carriers" who are Aa) and 0.01% will have the condition, while 99% of men will be "A" and appear normal and 1% will have "a" and have the condition. Thus, men are enormously more likely to get unusual recessive genetic conditions when the gene is on the X chromosome.
Colorblindness is one such condition, which comes to mind: https://en.wikipedia.org/wiki/Color_blindness
So, if we hypothesize that there might be lots of recessive genes that have "some" effect on behavior or personality or whatever we care about... If the genes are on chromosomes other than the X, then men and women will have equal variation. If the genes are on the X chromosome, then men will exhibit more variance, because more of them exhibit the rare condition (while a similar number of women are merely carriers of it). So, if we suppose that there are some important recessive genes on the X chromosome, then we would expect to see higher male variance due to that.