Perhaps Snape makes a derogatory comment about Hermione's intelligence or her Muggle - born status in the fanfiction. Hermione is very proud of her academic achievements and her heritage. Any slights in these areas would definitely make her lose her temper and yell at him.
It could be that Snape is interfering with Hermione's attempts to help a friend or protect someone in the story. If he stands in the way of her doing what she believes is right, her passionate nature would lead her to yell at him in anger.
One possible reason could be Snape's unfair treatment of Gryffindor students in the fanfiction. Hermione, being a strong advocate for justice and fairness, might not be able to tolerate his constant bias against her house. For example, if Snape gives Gryffindor students harsher punishments than students from other houses for the same infractions, Hermione would likely be furious and yell at him.