First off, he makes learning fun. From putting roller skates on Boggarts, to always having chocolate on him, to having a final exam that was an obstacle course, Lupin engaged his students with a great time. School isn’t always supposed to be fun. Sometimes it should be hard and boring, but you’ve got to lighten it up and let students play too. Lupin did this well.
But he also wasn’t afraid to challenge them. Great teachers don’t shy their students away from confrontation, but helps them face their fears and learn to overcome them.
Remember when Snape belittled and shamed Neville in front of the entire class. Lupin used this as a learning experience for him, and taught him to stand up to what he is afraid of.
But what made Lupin truly great is how he built relationships with students. His job was way more than just teaching content and making sure you could fight Volde-(Cut to John with stern face, then back to me)- He Who Must Not be Named. He cared and listened and related to his students. And in return, his students cared, listened, and related to him.
And the real magic in Lupin’s process of building relationships with his students is that they are then engaged in everything that he is teaching.
Harry learned complex magic from Lupin, skills he was able to use outside of the classroom, and eventually in his career later in life.
So wait, why isn’t this guy Number 1 on the list?
Good question, because he turned into a freaking werewolf and tried to eat his students!
That’ll keep you at number 3.