Why do most people assume that mages like taking on students?

A real mage works in solitude, like an artist. He is concerned with mastering his craft, downloading more and more knowledge from the astral realm, and breaching milestones for posterity.

Based on my observation, "students" steal (materially or intellectually), seduce, seek thrills, and strive for their own stardom. They probably saw too many "sorcerer's apprentice" movies. But no mage in his right mind would ever want to be surrounded with people like that.