Shut Up, Water BuffaloWhy do people use racial slurs? Because they work.
In the toolbox of Language, racial slurs are an easy shorthand; group a set of people (easily picked out by visual cues) into a set of expected shortcomings, and move on. Time is saved, and you never apply these shortcomings to yourself, meaning you can feel better than the group that doesn't get it and never will get it.
In a world where most words have lost their edges ("murder" and "pregnant" come to mind as garnering little reaction when used in conversation) a racial slur can pack all the punch it used to carry.
On the other hand, who reacts when they hear the phrase "Paddy Wagon" (a reference to Irish as criminals, always being picked up by police) or "Indian Summer" (which references a summer turned cold, derived from "Indian Giver", a claim that american Indians would take back what they promised)?
If the goal is to quickly end a conversation and waste no more time on discussion, a good solid racial slur will bring things to a halt. In one word, you can show both an unwillingness to hear another view and a clear demarcation of where you think the others stand compared to you (far below). One does not name vermin; one calls them, simply, vermin. That tone continues to this day.