Saying "women should not lead" is a broad and vague topic to me.
It is like saying, "I don't drink". What the speaker actually means is that he is not drinking alcohol. 
For example who leads the kids when I am not home?
Who leads the classroom?
What business does a man have teaching a group of women, especially if his wife is not present?
You see, to me, when I am not home, my wife leads my children and she gives the instructions I gave her to the workers in our business. So in that way she leads. So if my son doesn't submit to his mother, he rebels against me and I will discipline him when I get home. If I told Erin to tell the carpenter what I want him to do and he dismisses my order that comes via a woman, I will deal with him. Usually, when that happens my wife says something like this: "I am just a messenger and I gave you the message and I can understand that you don't want to do it, so you are welcome to take it up with Jannie."