Story 1: A man own a house. His girlfriend had recently moved in and he wanted her out. She refused and called the police, claiming that the man committed violence against her. Also he reported that the woman was actually harassing him, the man was still immediately removed from the house and he had to pay a huge amount of lawyer fee before moving his ex-girlfriend out. The woman did not even provide actual evidence on the "violence".
Story 2: In a formal organizational event, everyone dressed formally, except one woman.
Man: "I am not sure if you are dressing like in a night-club."
The woman reported it as "sexual harassment" to the supervisor and the man is seriously punished. But if a woman said something similar to a man and the man reported it to the supervisor, it would be usually ignored as "not a big deal", to my limited knowledge.
Thanks for the comments! From the legal document of John Doe v.s. Rhodes College 2019, it is clear that the college's administrators took the words from female witnesses (including the victim) but not from the male witnesses, at least in this case:
I hear similar stories every once a while.
So, is the woman privileged (legally or statistically) in a conflict between a man and a woman, either inside an organization or in the court?