It could also be a sacrifice play. Peter might have believed that by jumping off the building, he could draw the attention of a powerful villain away from his friends or the city. He is known for his selfless nature, and sacrificing himself in this way could be a way to protect others.
One possible reason could be to save someone. Maybe there was a threat in the building that he could only stop by jumping off and using his powers in mid - air. For example, a bomb was about to go off and the only way to defuse it was to jump from a certain angle.
Perhaps he was under the influence of some mind - controlling device or magic. He might not have been in his right mind and thought that jumping off the building was the right thing to do. It could be that an enemy had managed to manipulate his thoughts to make him take this dangerous action.
Peter's own quick thinking helps him survive. He could use his surroundings during the fall. For example, if there are ledges on the building, he can use them to break his fall. He can also calculate the best way to land, using his acrobatic skills that come with his powers, so that he minimizes the damage to himself.
Perhaps in this fanfiction, Peter has some new power or gadget that he's testing. So when he jumps off the building, instead of the usual web - swinging, he activates this new ability which allows him to fly or at least glide to the ground in a very cool and unexpected way.
One possibility could be that Peter is extremely stressed at school. Maybe he's being bullied or facing overwhelming academic pressure. So, in a moment of despair, he jumps off the school roof. But then, he could miraculously survive and this event could be a turning point for him to face his problems and seek help.
His best friend could be a main character. This friend might be the one who tries to understand why Peter did it and be there for him during his recovery if he survives. Maybe the friend was the only one who knew Peter was struggling before the jump.
One possible reason could be a misunderstanding. Maybe Peter overheard something Tony said and misinterpreted it as a sign of mistrust or dislike. For example, if Tony was talking to another character about Peter's abilities in a way that Peter thought was critical rather than constructive.
Well, it could be that Peter starts off as a regular guy who is just a huge fan of the Avengers. Maybe he follows all their news, collects their merchandise. One day, he gets a chance to meet them somehow, like through a Stark Industries internship. Then he gradually proves himself useful to them and they start to train him. Eventually, he becomes part of the team, with his own unique skills like his spider - powers adding to the Avengers' strength.
Peter could be an ordinary person who has been given extraordinary powers for some reason in this fanfiction.
Maybe Peter discovers a group of ducks that have some sort of special power or connection to the Avengers. And he decides to protect them from villains who want to use them for evil purposes.
He could be trying to save someone. Maybe a civilian is falling from a higher floor, and Peter jumps off to catch them and use his webs to swing them to safety.
It could be that Peter is in a world where he's constantly challenged to show his extreme power. Lifting a building could be part of a test or a show of his capabilities to other characters in the fanfiction. He might be doing it to prove himself worthy of something, like joining a special group or impressing a love interest.