Also an important thing to note is that Aurors are not cops/police. The Magical World operates differently than the muggle one, and the law enforcement there has it's own bits. Aurors are closer to special-force detectives, they are trained to investigate and fight dark magic specifically.
Magical Law Enforcement Patrol is something much closer to regular police:
Arthur Weasley: "I only hope we can catch whoever’s doing it."
Harry Potter: "Will it be Aurors who catch them?"
Arthur Weasley: "Oh no, this is too trivial for Aurors, it’ll be the ordinary Magical Law Enforcement Patrol —"
A part of Magical Law Enforcement Patrol were also trained Hit Wizards and Witches, meant to help with high-risk arrests, riot control and were often called as help for Aurors to detain Dark Wizards.
Harry is more like a magical detective rather than a policeman.
Another thing I often like to say when it comes to the "he should have been a teacher" discussion is that Harry spent most of his life in fight-flight situations. The boy was high on adrenaline a lot, even before Hogwarts ( with Dudley's gang playing Harry Hunting ). After the war Harry joining Auror forces is like him looking for a familiar environment, where he gets the adrenaline rush in a more controlled way. You could argue that a quidditch career would fit him better, if he needs some adrenaline in his life, but then we can't forget that a big part of who Harry is, is the fact he wants to save people. Harry wants to help, to fight, to make the world better.
Plus let's look who Harry's role models were:
His father, Sirius, Moody, Tonks, Dumbledore - An Auror career was something he wanted ( “Yes?” Professor McGonagall prompted Harry. “Well, I thought of, maybe, being an Auror,” Harry mumbled. ), and also something a lot of people encouraged him for. Meanwhile not only was teaching the DA thrust upon him ( and after it ended Harry expressed no interest in picking it back up ), it was VERY different from an actual job. Teaching purely practical spells to a group of motivated teens, most of whom were his friends, is WAAAAY different than teaching a curriculum of theory & practice, assigning homework and grading papers for seven years of students at once.
I don't understand why Harry becoming an auror is still a talk this fandom has.
