It could be due to a conflict with another student in the potions class. Maybe they bullied him or said something really mean. And sometimes in fanfics, there could be a hidden prophecy or curse related to potions that makes him emotional and cry.
One reason could be that he's facing extreme pressure in potions class. Maybe he's constantly compared to others, like Snape always having high expectations of him. Another reason might be that he has some kind of emotional turmoil related to his past traumas while in the potions environment. For example, the smell of a certain potion might remind him of a difficult time at the Dursleys.
Perhaps he's having trouble with a particular potion recipe. He could be worried about getting a bad grade or disappointing his friends. Also, there could be some kind of magical interference in the potions classroom that's causing him distress and making him cry.
Maybe he was poisoned. There could be someone who slipped a harmful potion ingredient into his cauldron without him noticing. It's a common plot device in fanfics to create drama.
It could be that he has a bad accident in the potions lab. For example, a potion explodes and nearly kills him or one of his friends. This traumatic experience makes him lose his confidence and interest in potions, leading him to quit as seen in some fanfictions.
Maybe Snape wants to train Harry better. By using potions to change Harry's abilities or characteristics, he can expose Harry to different challenges and make him a stronger wizard. For instance, if he gives Harry a potion that temporarily takes away his ability to use magic, Harry will have to learn to rely on other skills.
Maybe Harry is crying because he misses his parents. He often feels the pain of their absence deeply, and in this fanfic, when Sirius sees him, that could be the cause.
Perhaps he was extremely tired or stressed. Harry has a lot on his plate, with Voldemort constantly being a threat and all the schoolwork and Quidditch. He might not have had enough sleep or rest, and the potions class was just the tipping point where his body gave out.
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.
One possibility is that a potions accident could cause a time - related mishap. Maybe the potion was supposed to be a simple Sleeping Draught but due to the accident, it creates a time - loop. The characters find themselves repeating the same day over and over until they figure out how to reverse the effects of the botched potion. This could be a really interesting plot device in a Harry Potter fanfic as it would allow for a lot of character development and exploration of different choices within the same day.
Well, it could be that he's feeling the weight of his destiny. Harry has so much on his shoulders, like fighting Voldemort. Maybe he just had a particularly tough encounter with the Dark Arts or lost someone dear in the fight against the dark side. Another reason might be his feeling of isolation. Despite having friends, there are times when he feels alone in his battle.
He might hide it because he doesn't fully understand his own fascination. Harry has always been on the side of good, but perhaps there are elements of the dark side that seem alluring in a strange way. He could be afraid that exploring these feelings would lead him down a dangerous path, so he keeps it a secret.
Hermione would be a likely candidate. She's always been there for Harry and is very empathetic. She would probably offer him some words of wisdom and a shoulder to cry on.