For example-Women have better social skills (good!), but are more prone to depression (bad). Men are better self-promoters (good!), but are more aggressive (bad).

Wouldn't keeping these two examples symmetrical be better? Depression while it does affect others primarily hurts the person who is depressed, inappropriate aggression while it does affect the person engaged in it, primarily hurts others. Implicitly this affirms the axiom that average women are more valuable than average men, which is ingrained in us to a surprising extent.

There are plenty of examples of male traits that hurt men. Higher suicide rate for starters.