Not true. Some men scheme. You have full TV shows illustrating this. For example House of cards.

In many workplaces, there are men talking about other men to get ahead. They can also talk about other women.

For example, at high school that when a girl rejects a man, that she is called "a slut". And her reputation would be ruined even if it is a lie and there is no proof. And since she would be considered a slut, she would be harassed.

The point is, some people do this regardless of gender. And men do it more frequently than people think. We are just trained to ignore it.