Uncle Andrew is a magician. He’s done much experimentation and explored many mysteries to get to where he is, and he’s quite proud of his accomplishments.
What’s more, he’s quite proud of himself in general–even without accomplishments to back him up. He describes himself to Digory as a man “who possess[es] hidden wisdom.” Once away from the terror of Jadis, he begins to think himself a rather “distinguished-looking man”. “‘Andrew, my boy,’ he said to himself as he looked in the glass, ‘you’re a devilish well preserved fellow for your age.'” When he finds himself in Narnia (by no act of his own) and observing a miraculous creation event, he is still full of his own greatness–“Ho, ho! They laughed at my magic….I wonder what they’ll say now? I have discovered a world where everything is bursting with life and growth. Columbus, now, they talk about Columbus. But what was America to this?”
Ultimately, though, Uncle Andrew’s “greatness” (or at least his perceived greatness) is an excuse to do whatever he likes without regard for rules or relationship. Digory had this figured out by the second chapter. Uncle Andrew says “But of course you must understand that rules…however excellent they may be for little boys–and servants–and women–and even people in general, can’t possibly be expected to apply to profound students and great thinkers and sages…” After hearing Uncle Andrew’s monologue, Digory reflects: “All it means…is that he thinks he can do anything he likes to get anything he wants.”
Andrew selfishly regards himself as great, while taking liberties with the lives of others. Asked why he did not travel to the other world himself, Andrew answers: “Me? Me?…A man at my time of life, and in my state of health, to risk the shock and the dangers of being flung suddently into a different universe?” For him to take risks for his magic would be preposterous–but he has no qualms with sending Polly and Digory where he himself would not go.
In Uncle Andrews mind, greatness means being above the law. For him, greatness means having the right to do whatever he pleases, never mind the consequences to others.