So, maybe male privilege exist, but so do female privilege:

In my childhood girls were never beaten. Boys were by each other.

During my studies girls got extra study points for higher education - just for being girls. IIRC this held true even for studies who were mostly girls anyway, like nurse and chemistry. (This has been fixed to some degree now I think so boys will now get extra study points if they apply for nurse studies.)

At work they count and celebrate how many women we have. In a way it feels obvious since we want equality. But lets not pretend it's 50/50 if two equal candidates come through the door and hiring one of them will make your stats look nicer.