Perhaps in the fanfic, Draco says or does something that deeply affects Hermione on a personal level. For example, he might accidentally reveal a truth that shatters her world view. Since Hermione is a very intelligent and strong - willed character, when her beliefs are shaken, it could lead to an emotional breakdown like crying.
One possible reason could be a sudden outburst of pent - up emotions. Maybe Hermione has been bottling up her feelings for a long time, and in the presence of Draco (in the context of the fanfic), something triggers her to break down. It could be a situation related to the ongoing conflict between Gryffindor and Slytherin in the Hogwarts setting, and Draco represents all the stress and frustration she has with that divide.
It could also be due to unrequited love. If the fanfic takes a romantic turn, Hermione might have developed feelings for Draco, which go against all her previous notions and the social norms in the wizarding world. The internal struggle between her heart and her mind could become too much to bear, causing her to cry in front of him.
Draco might be initially shocked. He's used to seeing Hermione as a strong adversary, so seeing her cry would be unexpected. He could just stand there, not knowing how to react at first.
Maybe Harry is under a great deal of stress. He has so many burdens on his young shoulders, like fighting Voldemort, protecting his friends, and dealing with the secrets of his past. Snape has always been a rather intimidating figure to him, but in that moment, the pressure might just be too much, causing him to break down in front of Snape.
Perhaps he's had a falling - out with his friends. In the Slytherin house, there could be a lot of power dynamics and rivalries. If he's been betrayed by someone he thought was a friend, it would be very upsetting.
One reason could be Snape's sense of justice. Despite his often - cold exterior, he might not tolerate Draco's bullying behavior towards Hermione.
One reason could be the stress of fighting Voldemort. Harry has so much on his shoulders, and McGonagall is a figure of authority and comfort. He might break down in front of her when the pressure becomes too much. For example, when he has to face difficult decisions like whether to sacrifice himself or when he feels responsible for the safety of his friends.
It could be a plot where Draco and Hermione are forced into a situation where they have to rely on each other's knowledge. Their 'tongue' in this case might refer to their quick - wittedness. For instance, they might be in a magical maze and need to solve puzzles by using their combined intelligence, which then leads to a new - found respect for each other.
One possible plot could be that Hermione is captured and brought to the Malfoy Manor. Draco, having some internal conflict due to his growing feelings for Hermione despite their past enmity, tries to protect her from the other Death Eaters in the Manor. Maybe they end up having to work together to escape some dark magic trap set within the Manor.
She could be defiant at first. Hermione is a strong - willed character, so she might immediately start trying to escape or use her magic against Draco. She could also try to reason with him, asking him why he's doing this and trying to appeal to his better nature.
Maybe she's caught in a dangerous spell gone wrong. If a spell she or someone else casts backfires and starts to cause chaos around her, like objects flying at her or strange illusions appearing, that would be a valid reason for her to scream.
One possible reason could be the long - standing rivalry between Gryffindor and Slytherin. Hermione, being a Gryffindor, has always seen Draco as an adversary. So, in a fanfic situation where they are brought together in some way, her past experiences and prejudices might make her scared. For example, Draco has taunted her and her friends many times before.