One possible reason could be jealousy. Maybe Peter has some natural talent or ability that Tony wishes he had, and this makes him mean. For example, if Peter is really good at something like coming up with innovative ideas quickly, and Tony, who is used to being the smartest in the room, feels threatened.
One possible reason could be a misunderstanding. Maybe Peter accidentally gets involved in something that looks bad to the Avengers, like being in the wrong place at the wrong time during a security breach. So they misjudge him and are mean as a result.
Peter could stand up to Tony. By showing his strength and not taking Tony's meanness lying down, he might earn Tony's respect. For instance, if Tony makes a snide comment, Peter could give a smart comeback that makes Tony see him in a new light.
Another reason could be jealousy. In some fanfictions, Tony might be jealous of Peter's natural abilities and the way he is so quickly embraced by the public. Peter, in turn, could be envious of Tony's resources and experience. These emotions can fuel arguments between them. Their relationship is complex and full of potential sources of conflict like this.
In some fanfictions, Tony's possessiveness shows in more subtle ways. He might be possessive of Peter's time, always wanting to have Peter work on projects with him. He also could be jealous if Peter spends too much time with other people, especially if he thinks they might influence Peter in a way he doesn't like.
Well, it could be that in the fanfiction, they argue about technology. Peter, being the brilliant young mind that he is, might have different ideas on how to use or develop Stark tech compared to Tony. Tony is more experienced and perhaps set in his ways, so when Peter challenges him, an argument ensues.
One possible reason could be that Tony Stark is being overly critical of Peter's superhero work. Maybe Peter made a big mistake during a mission, and Tony's harsh words in his attempt to correct Peter made him cry. For example, if Peter accidentally put civilians in danger and Tony scolded him severely.
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.
One possible reason could be that Tony sees a lot of potential in Peter. In the original story, Peter has great powers and a good heart. The fanfiction might explore different scenarios of their relationship, like a mentor - mentee relationship in more depth. Tony might be interested in how fans envision their interactions and the growth of Peter under his influence.
One reason could be that Tony has a new project related to Peter's studies. He might want Peter to be involved in it, like a research project on some new material that could be used in Spider - Man's suit. So he calls him during school hours to discuss it.
Maybe Peter discovers that Tony has been keeping secrets from him that directly affect his life or safety. For example, if Tony has been secretly monitoring Peter without his knowledge, Peter might feel betrayed and cut ties.