It could be that Harry is framed for a serious crime within the wizarding world. Snape, being a respected (although grudgingly) figure in the wizarding community, might be the only one who can prove Harry's innocence. He has the knowledge and the influence, if he chooses to use it, to help Harry clear his name.
Maybe Harry discovers something about his past, perhaps related to his parents, that only Snape can help with. Snape was closely associated with Harry's parents. He might know some secrets or have some information that could help Harry understand a family mystery or some hidden power within him.
One possible reason could be related to a difficult potion she's trying to brew. Snape is a potions master, and Hermione might be facing an ingredient or a process that she can't figure out on her own. For example, a rare potion that requires precise handling of dangerous ingredients.
One possible reason could be his lingering resentment towards James Potter, Harry's father. Snape and James had a long - standing feud during their school days. Since Harry looks a lot like James, Snape might be transferring his old grudges onto Harry.
One possible reason could be Snape's long - standing grudge against James Potter, Harry's father. Since Snape had a difficult past with James, he might project that onto Harry. Another reason could be that Snape is trying to protect Harry in a very strange way. He may think that by rejecting Harry, he is keeping him at a distance from the dangerous wizarding world politics and plots that Snape is often involved in.
Maybe Snape suspects Harry of being involved in some sort of dangerous activity related to the Dark Arts. Pressing him to the wall could be a way to force Harry to come clean about his actions or any knowledge he might have. It could also be that Snape is acting out of his own insecurities and pent - up emotions towards Harry, which he has been suppressing for a long time.
One possible reason could be that Snape suspects Harry of something. Maybe he thinks Harry is involved in some sort of mischief or is in possession of something he shouldn't have. Snape has always been a bit of a mystery and is often distrustful of Harry, so this action might be his way of getting to the bottom of things.
One possible reason could be that Snape shows a different side to Harry in the fanfiction. Maybe he protects Harry secretly from some hidden threats that others are unaware of, which makes Harry start to trust him.
One reason could be a surprise attack by Voldemort or his Death Eaters. Maybe they found a way to bypass all the protection spells around Harry and launched a sudden, fatal assault.
Snape could be very sarcastic and cold at first. He might taunt Harry about finally coming to him for help. However, as he realizes the gravity of the situation, he could start to take it more seriously and actually use his skills and knowledge to help Harry. For example, he might say something like 'Potter, so you've finally realized that you're in over your head and need my help? Well, don't expect me to hold your hand.' But then he would still start to investigate the problem.
One possible reason could be that Snape is starting to see Harry in a different light. Maybe he realizes that Harry has been through a lot and has a moment of empathy. It could also be a sign of a deeper, unspoken connection developing between them in the alternate universe of the fanfiction.
One possible reason could be that Snape is trying to intimidate Harry. He has always had a rather tense relationship with Harry in the original story, and this could be an extreme form of showing his authority. Maybe he suspects Harry of something, like being involved in some mischief or having knowledge about a certain Dark Arts item or activity.