Spider-Man has definitely been in the Avengers in the comics. His presence has added a fresh dynamic and his powers and wit have been valuable assets to the group.
One reason could be a misunderstanding. Maybe some events were misinterpreted, and the Avengers thought Spider - Man was involved in something bad. For example, if there were some crimes that seemed to have Spider - Man's fingerprints all over them, but in reality, he was being framed.
Spider-Man has indeed joined the Avengers in the comics. This addition brings his unique skills and personality to the group, adding a new dynamic. His presence has led to some exciting storylines and team-ups.
Spider - Man would probably be defensive at first. He's used to working alone most of the time, and being interrogated by the Avengers would seem unfair to him. He might crack some jokes to ease the tension, but also firmly state that he's a hero too.
Captain America would be a likely candidate. He's all about justice and if he thought Spider - Man was doing something wrong, he'd go after him. Also, Iron Man. He's often quick to act and if he saw Spider - Man as a threat to his technology or the safety of the world, he'd be on the chase. Black Widow too, as she's used to tracking down targets and if she was given the order to bring in Spider - Man, she'd do it.
Their dynamics would change a great deal. There would be a lot more tension. Some members might blame themselves or others. For example, Iron Man could be at odds with Captain America if they had different ideas on how to handle the situation. Their usual teamwork might break down as they are all dealing with grief in different ways.