Perhaps it's his best friend who has some juicy gossip to share. But it's really bad timing as he's in class. His friend might not be aware of his class schedule.
Well, he might get in trouble with the teacher. Teachers usually don't like students getting phone calls during class. So, the teacher could take his phone away and give him a detention.
Well, it depends on who's calling. If it's Tony Stark, for example, Peter would be super excited and might not be able to hide it. He could try to come up with some lame excuse to leave the class, like saying he has a stomachache. But the teacher might not believe him. And his classmates would be curious about who's on the other end of the call.
There's also a chance that it could be a new superhero or villain. Maybe a new hero wants to team up with Spider - Man or a villain is taunting him, starting a new plot in the fanfiction world. This would create an exciting situation for Peter to deal with while trying not to blow his cover in class.
Perhaps it's a matter of time - sensitivity. Fury might not be able to wait until after class. There could be a time - critical situation where Peter's powers are needed immediately.
Well, in the fanfiction, perhaps it's a call from an old friend who needs his help. Dante might then gear up and set off on a new adventure to assist his friend.
In a fanfiction scenario, Peter Parker might be using his phone in class to check on the news about any recent crimes in the city. His friends notice him being distracted and start to tease him. However, little do they know that he's actually looking for signs of trouble so he can swing into action as Spider - Man right after school.
He could be using his phone to track a villain's movements. Maybe he installed some special app on his phone that can detect unusual energy signatures. So while the teacher is droning on about history or math, Peter is secretly following the path of a super - villain who is on the loose in the city.