Because it's so much simpler and easier to use. The metric system is an improvement over the English system in three major points: One unit of measurement for each physical quantity. No matter from which other quantities of the SI system derived, yields always the same unit.
The distance Hailey traveled is 12+12+16=40 meters. In fact, if you want to compute the distance you have to compute how many meters she walked. So, in this case, the direction she walked in doesn't matter.
The displacement, on the other hand, is the distance between the starting and finishing point. In this case, the 12 meters she walked in both direction cancel out, and the final displacement is 16 meters: she started from the classroom, she walks 12 meters (displacement: 12 meters), she comes back to the classroom (displacement: 0 meters), and she walks 16 meters (displacement: 16 meters)