dick-measuring contest

noun1

1. •
   (vulgar, figurative) A situation in which people (usually men) compete, often over superficial characteristics, to demonstrate their worthiness, power, etc.

   • “Because I'm a woman in a dick-measuring contest,” 6 says. “Business is a man's game, and they don't like me playing. Opening my mouth is a challenge to their masculinity.” — 2000