You would have to provide a quote or a source about the Buddha saying "never trust a woman" and about the Buddha setting up a "monastery/university".
I have never heard the Buddha said or did these things. My impression is the Buddha was a wanderer, who only lived in monasteries (set up by lay supporters) during the rainy season. This practise started because wandering monks could die from floods, etc.
My knowledge of Buddhism regarding marriage is the Buddha said a husband serves his wife in five ways. Upon being served (appropriately), a wife returns her love in five ways.
If you visit a Buddhist culture, such as Thailand, and see the real culture (away from the Vietnam War brothels), you will see women are expressive & assertive and men a deferring & quiet. Traditional Thai culture is generally matriarchial. This is Buddhist culture.
You sound confused and culturally ignorant.
But in brief, a man should feel shame when a women trashes him. He should use that shame for self-improvement.