It would be more likely that genetic factors for mental wellness are missing. Remember the Y chromosome is much smaller than the X and is simply missing many of the genes. Where someone with XX has 2 copes of each gene, someone with XY only has 1 copy of many or even most genes from that chromosome pair. This is also why you can't be YY, the X codes for things that you need to live and the Y doesn't have.
Take for example a mental disorder that appears with recessive genes. Generally if you have something that expresses recessively you need to have 2 copies of the recessive gene, one on each chromosome, for that trait to express. If you also have the dominant trait that means you are only a carrier. If the gene for this is on the part of the X chromosome that the Y doesn't have, that means that you have a higher chance of not getting the recessive gene if you are XX, because you might get the dominant gene from either parent that cancels the effect. If you're XY, that means you only get one copy of the gene. Your chances of getting the recessive depends on what your parents have, but if your mother is a recessive carrier and your father is not, an XX has no chance of expressing the recessive trait but an XY has it 50/50.
But you also get into weird things where if you're XY you can't inherit the recessive trait from your father because the Y doesn't carry it - you get your X from your mother. So It can pass from mother to child regardless of their chromosomes or from father to XX daughter. It can even skip a generation where Grandpa Andy passes the recessive X to his daughter Belle who then passes it to Andy's grandson Cody, who got the Y chromosome from son in law Dave which triggers expression of the trait which wouldn't have happened if Cody had got Dave's X chromosome instead. Dave doesn't have to have any family history of the recessive disorder for his Y chromosome to cause it to surface in Cody.tl;dr
Because the Y chromosome is missing a lot of genes it works like a wild card causing whatever is on the X chromosome in that missing part to manifest.
But you should note that recessive genes =/= disorder. Recessive genes can be anything, including basic things like pigmentation. Disorders often are carried recessively though because dominantly expressed traits are passed down in a very obvious way, and when people see a disorder or disability being passed down they tend to avoid doing that, which causes dominant-expressed disorders to become less common. Recessive disorders are harder to keep track of because they can hide for several generations.