Percy, with another feat of strength proposed, couldn't pass this up.

He just wanted to stroke his own ego-

Sort of. Percy mostly wanted to impress you. So, after Grover "challenged" him to a pushup contest(Percy bribed him to do so), he took it one step further and beckoned you onto his back with a flick of his wrist.

"Come on," Percy let a small smirk tug at his lips. "I can handle it."