Snape may be influenced by his own insecurities and jealousy. He has always had a difficult relationship with Harry, and taking him by force could be a way for Snape to assert his authority and show that he is in control. He might also be trying to prove something to himself or to others in the wizarding community, that he is capable of handling a situation as important as dealing with Harry Potter.
One possible motive could be Snape's complex relationship with Harry's father. Snape might see Harry as a way to get back at James in some twisted way. He could also be acting out of a sense of duty to the Dark Lord, believing that taking Harry by force is part of some larger plan to gain power or favor.
Another reason could be a build - up of years of pent - up anger and frustration. Snape has been harsh on Harry throughout his years at Hogwarts. Harry has had to endure Snape's unfair treatment, and all of that negative emotion could explode in a moment of extreme stress or danger, leading him to stab Snape.
One possible motive could be that Snape is still deeply influenced by his loyalty to Voldemort in this fanfiction. Maybe Voldemort has some hold over him that forces him to do the unthinkable. Another reason could be a misunderstanding. Snape might believe that Harry has turned to the dark side or is about to, and he decides to take preemptive action to stop what he thinks will be a great evil.
Perhaps the plot is centered around Snape having some sort of misinformation. He takes Harry by force because he thinks Harry is in danger and he needs to protect him in his own way, which is rather forceful. This could lead to a lot of conflict between Harry and Snape initially, but then they might come to understand each other's motives as the story progresses.
Snape could also be acting out of a sense of justice. Lucius was a Death Eater, and Snape, despite his own past as a Death Eater, had turned against Voldemort. Saving an innocent, especially Harry's daughter, from Lucius would be in line with his new allegiance to the side of good.
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.
Perhaps in the fanfic, Snape discovers a powerful and dangerous magic that he wants to use for what he believes is the greater good, but Harry sees it as a threat. Harry has always been wary of Snape, and this new discovery could be the tipping point. Also, if Snape were to make a deal with a dark force in order to gain knowledge to defeat Voldemort but Harry misinterprets his intentions, it could lead to Harry killing Snape.
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 motive could be a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
One possible reason could be punishment. Snape has always had a rather thorny relationship with Harry in the original series. He might see this as a way to assert his authority over Harry. Maybe Harry has done something in the context of the fanfiction, like accidentally messing up Snape's potion ingredients or getting into an area of Snape's house where he wasn't supposed to be.
Initially, the relationship is one of captor and captive. Snape is in control and Harry is the unwilling victim. But as the story unfolds, Harry might begin to question Snape's motives. Snape, in turn, might start to open up a bit about his reasons for taking Harry. This could lead to a slow transformation of their relationship. They might find common ground in their shared experiences, such as both having lost people they loved to Voldemort. This newfound connection could start to heal the rift between them.