There’s no evidence in Quran that prohibits women from becoming leaders, presidents, governors, etc. However, there’s evidence on that men are created more suitably on guarding other people.
Allah the Almighty commands:
“Men are guardians over women because Allah has given different capabilities to one another, and because they spend of their wealth. Good women are obedient (to Allah), and guarding of the privacy for Allah has guarded them. (…)” (The Women 4:34)
The main principle of administration is guarding. Considering that Allah has made men responsible for guarding and administration of the family, we can say that men’s disposition is more likely to be successful on these issues. Therefore, Muslims should consider this fact on electing their leaders and governors, because Allah says:
“Allah commands you to deliver trusts to those worthy of them. (…)” (The Women 4:58)