gale had so much ambition that even being close/ in love/ the muse of mystra wasnt enough and he tried to get more and more and more magic power. When he asked mystra to show him more of the weave and she said no be content and in response he tried chasing down ancient magic with near 0 understanding of it. His crime was unbridled ambition in the face of a life anyone else in his circumstances wouldve been more than happy. Gale went against the goddess of the weave and his punishment is..... a teaching job..... just my 2 cents i know its not everyones opinion or even a popular one but between that and the way he talks he just gets on my nerves.
He was a gifted child who, while clearly loving his craft, magic, was also made to feel it is the only thing valuable about him. He is also a wizard, so he did work for his great magical skill and his position. So yes, to prove himself worthy to his lady love to become and even better wizard, he tried to get something for her that turned out not to be the thing he expected. His punishment for that was, that he lost all or most of his magical skill (again the thing he worked for all his life), his lover did not talk to him anymore, he became actively dangerous to be around and spend a year alone in his tower because he had nobody to turn to but his cat. When you bring him to his good ending, he either becomes a teacher who actively tries to foster a better work-life-balance in his students, helps to rebuild the Gate or becomes an adventurer who helps people just for the sake of it. In each of his good endings, he is happy but a lot of this happiness come from helping others in some way. That is a pretty nice character arc.
I can get why people find him annoying but searching for some great "crime" to justify that dislike with morale is like saying Shadowheart should have seen through Mother Superior's game, Astarion should have stood up to Cazador more or Karlach should have not trusted Gortash.