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You're right. Estrogens play an important role in brain development. They stimulate a few regions in the brain, which include parts of the limbic system and the frontal lobe. Both playing a huge role in emotional stability and impulse control.

Now what we see in both primates and humans, is that when males get frustrated, they will seek out a weaker opponent to unleash it on. This usually is a juvenile or their mother. Females are weaker, and don't have many targets to terrorize. They absolutely would if they could. So estrogens play a role in self control.

Women inherited this benefit. The emotional and cognitive control that estrogens enhance, is why women are less impulsive, have lower expression of aggression and perform much better in schools. This is because estrogens stimulate brain development in girls and it gives them an advantage over boys.

We also found that men with normal testosterone levels have this effect too. In pretty much all animals where we studied this, higher levels of testosterone correlate with higher levels of aggression. Not only that, in both humans and rats, t-levels fluctuated based on social hierarchy. Changing as status changes. This may have to do with self preservation and making sure you don't piss off a stronger opponent.

But in humans, slightly higher levels of testosterone correlate with less aggressive behaviours. This is because when men and women produce more androgens, they produce more estrogens. And so the self-control for men increases.

Furthermore. Women who take the contraceptive pill are twice more likely to attempt suicide and 3 times more likely to succeed than women who don't take the pill. This is why estrogens are added to prevent depression. A well known side effect of the pill.