That's one of the questions that has bugged me since Episode 1: What is it with the threehorns? Why are they so self-centered and convinced they are better than everyone else?
Their role is obviously that of representing the bigots in society today, the people who look down on everyone not as fortunate as them, and act snobbish and whatnot.
But for the sake of the series? My guess is that it's all territorial. In the Great Valley, populated by mostly herbivores, Triceratops are at a huge tactical advantage over everyone with their horns, and strong and bulky build. Thought at the same time they are not invincible, and are grossly outnumbered, so they probably give off the arrogant and bossy air just to keep people who they perceive as a threat to them in line, and thus assert their dominance.
