‘The antler dance’, ‘locking horns’, ‘butting heads’: I don’t think these are exactly the right way to describe what I’m thinking of.
What is it called when two men, both fairly dominant in their everyday lives, meet for the first time, maybe at a social event, maybe accompanied by their wives, and the men have a session of questioning and boasting to see which of them has higher status?
It’s fairly subtle; nobody’s raising his voice, losing his temper or swinging punches. Their wives probably notice what’s going on (and ‘hear the testosterone bubbling’, as they say). The men may not even realize they’re engaged in some sort of challenge or duel, and it may not stop the men becoming friends afterwards.
What’s the right phrase for this?
As is often the case with male behavior, there are multiple rude ways of saying this.
Another crude expression is dick-measuring contest.
In both cases the emphasis is on behavior which is specifically associated with males and competition.