Our proof that women should not lead men is very simple:
When human beings lead they control. Human beings should not control other human beings. Therefore, human beings should not lead other human beings. Therefore, women should not lead other human beings. Therefore, women should not lead men.
Now, civilized societies are complicated, meaning a rule might have one or more exceptions. In the case of women leading men, there are two exceptions:
Exception 1: Legal Insanity
Human beings may lead other human beings if the other human beings are legally insane; that is, if the other human beings cannot stop themselves from physically attacking themselves and/or one or more other human beings.
Exception 2: Covenant (Divinely Approved Agreement)
Human beings may lead other human beings if the other human beings have agreed to be lead by the former (first mentioned in this sentence) human beings. However, note that God in the Bible teaches that men should never agree to be led by women (see, for example, 1Timothy 2:12, which says: “But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.”).