Why did they make Mercury dimes?

It was purely an artistic decision. The so-called "Mercury" design was adopted in 1916 as part of a general redesign process. Up till that year dimes, quarters and half dollars usually carried the same images. While there was little chance of confusion due to the coins' different sizes it was felt that separate themes would allow for more artistic creativity.

The noted sculptor A. A. Weinman had two of his proposals selected for the new coins: the famous "Walking Liberty" image was chosen for the half, and a classically-inspired image of Miss Liberty wearing a winged Liberty cap was chosen for the dime. When the dime entered circulation many people thought that the winged cap looked so much like that worn by the Roman god Mercury that they almost immediately started calling the coins "Mercury dimes", and the name has stuck ever since.