Symbolism, Imagery, Allegory
You Can't Spell Paladin without Pal
Every school worth its salt needs a solid mascot. They run the gamut from normal animals, like jaguars and bears, to weird objects, like pretzels, watermelons, and sentient polka dots (source).
The Center has a Paladin, which is somewhere in the middle of the normal-to-weird spectrum. Here's how it rolls: "A life-sized bronze statue of the school's mascot, the armored knight pictured in the Center's escutcheon, stood outside the entrance" (21.2). The Paladin carries a shield. On the shield is a coat of arms. And on the coat of arms is an image of the knight himself. Yes, the knight carries a picture of himself. A school full of people who think they are the best in the world has a narcissistic mascot. Very appropriate.
Near the end of the novel, Nick is pursued by a sentient version of the statue. It is slow, determined, and unstoppable, like the villain of a slasher movie. It also has superhuman strength and doesn't have to breathe underwater, yet the protagonists think, "It was somebody dressed up as the statue" (26.29). The Paladin must not be a mascot of critical thinking, because in a world full of magic, technology, and monsters, this is obviously the statue come to life.
And we can't let you go without mentioning that the legend of the paladins is actually real, at least in the sense that Frost didn't make just make it up. The twelve paladins were supposedly the best knights in Charlemagne's army, and the story of the re-conquest of Spain from the Umayyad Empire in the 8th century can be found in epics like The Song of Roland and Orlando Furioso.