Ha, actually I found out. That short story in the English test from years ago is called 'A Piece of Wood' by Ray Bradbury, and funnily enough, so is the quote -
"But after that," the sergeant said. "After they realized it was true, that every nation was disarmed and there was nothing more to fear, if we were all clean to start over fresh and new, what then?" "They'd rearm as swiftly as possible." "What if they could be stopped?" "Then they'd beat each other with their fists. If it got down to that. Huge armies of men with boxing gloves of steel spikes would gather at the national borders. And if you took the gloves away they'd use their fingernails and feet. And if you cut their legs off they'd spit on each other. And if you cut off their tongues and stopped their mouths with corks they'd fill the atmosphere so full of hate that mosquitoes would drop to the ground and birds would fall dead from telephone wires."