Why did a great mathematician call Cantor a corrupter of youth?

Because Leopold Kronecker thought Cantor was teaching a younger generation of mathematicians ideas that had no place in mathematics, above all the idea that a completed infinity is a real object. Cantor's set theory was controversial at the start, but it later became largely accepted, and most modern mathematics textbooks now implicitly use his views: a line is the infinite set of its points, and there are more real numbers than rational numbers.

Kronecker, who headed mathematics at Berlin, was his fiercest opponent. His opposition was public and personal: he described Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth". Behind the insults was a real principle. Kronecker, now seen as one of the founders of the constructive viewpoint in mathematics, disliked Cantor's set theory because it asserted that sets exist without giving specific examples of them. He is quoted as saying that God made the integers and all else is the work of man. For him, accepting actual infinity would open the door to paradoxes that would challenge the validity of mathematics as a whole.

He was not alone in thinking that infinity was a manner of speaking. Before Cantor, the infinite was deemed to have at most a potential existence rather than an actual one. Gauss's view is paraphrased as "Infinity is nothing more than a figure of speech which helps us talk about limits." Three schools of thought opposed Cantor on this point: constructivism and its two offshoots, intuitionism and finitism.

Cantor paid a price. His recurring bouts of depression from 1884 have been blamed on the hostile attitude of many of his contemporaries. But Cantor's ideas were ultimately largely accepted, strongly supported by David Hilbert, who predicted that no one would drive mathematicians from the paradise Cantor created.