battle of the sexes

noun3

1. •
   The persistent state of rivalry, opposition, or tension between men and women in society.

   • And when she returns to the battle of the sexes, she can state the situation in its starkest terms—"I hurt you/'cause you hurt me." — 1984
2. •
   Any competition between men and women.
3. •
   A situation in which two people want to do different things, but do them together.