Suppose you are taking a math exam. One about advanced calculus that is really hard and taxing. I'm talking about one of those that is five hours long and there are only three problems in total on the test, so you are expected to spend over an hour on each problem.

Would you prefer if a) the environment was quiet and no one was interrupting you. Or b) the environment was noisy and you were constantly interrupted by people talking about how they spent their weekend.

To many developers, productive work is like taking a math exam. Therefore we want the same kind of environment (a distraction free one) to do our best work.