Maybe the reason that men are allegedly more psychologically stable is because they are paid more. Financial instability is very stressful. Plus, more men than women are pedophiles and serial killers. Don't forget that. :-)
Me, I think kids need to grow up with a mom AND a dad. Married, stable couples are the ideal...and if the marriage doesn't work out, joint custody should be the default. That's just my opinion, though.
I was looking for the original study, because I recall seeing it as well, but couldn't find it. However, I also recall the criticism of that study. Given the current biases in our Family Law system, a father needs to fight, and hard, to gain custody of the children. Those who are willing to put in that much of a fight are generally likely to be committed parents. So the problem came from the self-selection - custodial fathers are most likely highly committed parents, while custodial mothers may or may not be.
However, your second comment, about men being more likely to be pedophiles and serial killers, does deserve some comment. Basically, that women are the more likely to abuse or kill their own children. Obviously, in either case, the man or woman is both an exception, and very deeply disturbed. However, men are more likely to turn their perversions outward, women are more likely to turn them inward.
Drew Garrett