Assalamu walaikum. I have a debt, I read here, that for important reasons a woman can lead prayers at home to her family members, but why can't she in mosques? Why aren't there women leading prayers inside mosques? (I know there are many men guiding prayer, but wanted to know about women on this spiritual side) jazak Allah
Alaikumassalam wa rahmatullah,
The Islamic social system is designed in such a way that men are the caretakers and protectors of women, so in things like prayer it is more natural for the men to be the leaders. For more on the Islamic social system regarding gender please see: A new approach to the Quran’s “Wife-Beating Verse” (al-Nisa 4:34)
As for the spiritual reason: Men and women have the same souls as far as we know. But they have different brains and genetic instincts, which requires the religion to treat them differently. This is why women have to cover their hair while men don’t have to. The way men experience their interactions with women is different from the way women experience their interactions with men.
As for the exact scientific reason why it’s better for men to lead prayers, I cannot say exactly what it is. To fully find out we’d need studies of communities where men lead the prayer and communities where women lead the prayer so that we can compare the results.
But since this is what the Prophet 
recommended, we are happy to go along with it. It is similar to accepting the ban on eating pork even though there are no detailed reasons for the ban in the Quran or hadith. If God commands us to do something, we obey, because we know He has our best interests at heart. We read the Quran and can see that it is really from God because of the intelligence and beauty in it. Once we are convinced that the Quran is really from God, then we don’t need proofs for everything in it (such as the ban on pork), we accept it based on the fact that we have agreed that the Quran is really from God and that God wants us to avoid pork.