The Daeodon pictured below is a type of entelodont. Their teeth are frightening if you get close up. For those of us lucky enough to be able to touch them, we know they're as sharp as a high-quality chef's knife.
This specimen (pictured) is in the Carnegie Museum. Why they have those big flanges is unknown for certain. When there’s a physical attribute like that, all paleontologists can usually do is make a sensible guess based on logic and by observing animals of today. As there’s no obvious hunting purpose to the flanges, the best guess is that it’s probably part of some male-male competition event over females or herd leadership...that is, if they’re only on males. We don’t know yet if that’s so. It takes complete skeletons to know their sex, and there simply aren’t that many of those. If the females all have flanges too, then either there was a lot of head butting or posturing among entelodonts (or intraspecies displays, as they are called), or they evolved for other reasons. For some reason, Nature selected for bigger flanges, and that usually means it helped individuals with bigger ones survive better or eat better or spread their own genes better by being the hottest entelodont in the neighborhood.
|Shot by Matt Celeskey via Wikimedia Commons