Ladies can read, ladies in prayer. There is no harm. But because Islam also teaches segregation of sexes and does not want human attention to be diverted to other channels than just the religious challenge and worship of Allah. And it is not a reflection upon ladies that they are not permitted to lead men. It is a reflection upon men that they are so perverted, some of them at least, that when the ladies lead the prayer, instead of remembering God, they would start thinking of their beautiful wives. So the whole purpose of worship would be defeated, frustrated. That is the reason why.
