He’s so young here. A petulant teen trapped in an old man’s body. He is raw and rough but so full of life. He can’t get back to Gallifrey just yet, but he knows the orange sky and silver trees are waiting for him. He hasn’t yet suffered the pain of regeneration, where he dies and a new man with dubious fashion sense (it took him centuries to rediscover his love of bowties) goes off in his place. He hasn’t lost companions, or ruined lives, or lost everything in the Time War; he still sees himself as a force of good. He does not yet have the blood of whole species, including his own people, on his hands. He is still so young. So when Barbara and Ian first arrive, all authoritative and knowing what is best for his Susan, he bristles at them (maybe the 20th century wasn’t the best place to send Susan to school, but that pigheaded fool Socrates refused to teach a girl). They are the authority he’s been running away from all his life. Someday he will be an old man in a young man’s body, but not now, not yet, and so he decides to take Ian and Barbara for a little spin, to knock them down a peg, to shake them out of their boring old adult ways. He is so, so young.