Aizawa may also interact with Izuku's family during family events or gatherings in the fanfic. He could be a guest and during that time, he could share his insights on Izuku's growth and development. This would not only strengthen his relationship with Izuku but also with his family as a whole.
Aizawa is known for his strict and somewhat reserved nature. This would have a significant impact on Izuku. Izuku, who is often eager and a bit impulsive, would learn to be more patient under Aizawa's guidance. Aizawa's ability to see the potential in his students despite their flaws would also make Izuku more confident in his own abilities. He would know that his father figure believes in him, and that would encourage him to keep pushing himself. Moreover, Aizawa's dry sense of humor might also influence Izuku's own sense of humor, making him a bit more sarcastic in a light - hearted way.
In some fanfictions, Aizawa might be under the influence of a villain's quirk that makes him act against his will. So, he kidnaps Izuku, but later on, he realizes what he's done and tries to make amends. This could lead to a story full of drama and redemption.
It could be Aizawa himself if he's being controlled by something or has some sort of ulterior motive that is not in Izuku's best interest. But if not Aizawa, then there could be a hidden villain who is manipulating Aizawa to kidnap Izuku.
Definitely. A lot of fanfic writers are attracted to this idea. They might create scenarios where Aizawa's no - nonsense attitude as a brother helps Izuku become more confident. Or perhaps there are fanfics that deal with the family dynamics between them and how it affects their respective roles in the hero society. Searching through the relevant tags on fanfic websites should lead you to some great reads.
Well, if Aizawa was Izuku's father, it might change how Izuku approaches hero training. Aizawa's no-nonsense attitude could make Izuku more disciplined from a young age.
One scenario could be that Izuku is on the roof to get some fresh air and clear his head. Aizawa, being the observant teacher he is, follows him there. He could then share some of his own experiences with Izuku, like how he overcame difficulties in his youth, which would inspire Izuku and strengthen their relationship in the fanfiction world.
Some dedicated My Hero Academia fanfiction forums might also have these stories. You can join these forums and ask around. Members are usually helpful in pointing you to the right stories.
One good one might be 'Aizawa's Guidance for Izuku' which focuses on their unique mentor - mentee relationship evolving in an interesting way. It has great character development.