“Let’s say that I taught them chess instead of English,” she says. “Every conversation would be a game. Every idea expressed through opposition, victory, defeat. You see the problem? If all I ever gave you was a hammer ...” “Everything’s a nail,”
This quote means that if Louise Banks were to teach aliens chess instead of English, every time they communicate with each other it will be aggressive because chess is a vicious game. All they're thinking about is defeating one another.