Maybe Snape is being controlled by some dark magic or a curse that makes him act this way against his normal nature.
Snape could be acting out of a sense of possessiveness. He has always had a complex relationship with Harry. In this fanfiction scenario, perhaps he has let his envy or some long - held grudge against James Potter (Harry's father) get the better of him. He might think that by forcing Harry into this situation, he can somehow get revenge on James through Harry, which is a very twisted way of thinking.
It could be that Snape has some deep - seated, warped idea of protecting Harry in an extreme way. He might think that by keeping Harry close in this inappropriate manner, he can shield him from other greater threats. Another possibility is that Snape is being influenced by some false information or a misunderstanding that has led him to believe this is the right course of action, even though it's clearly wrong.
Well, Harry is a brave character. So, he would probably be full of anger and disbelief. He might start yelling at Snape, demanding an explanation for such an inappropriate act. He would also be thinking about how to escape and report this to his friends or the proper authorities in the wizarding world, like Dumbledore.
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.
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.
One possible reason could be to protect Harry. Snape might believe that by tying Harry to the bed, he can keep him in a safe place away from immediate danger. Maybe there's a threat in Hogwarts or outside, and Snape thinks this extreme measure is necessary to ensure Harry's safety.
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.
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 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.
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.
In some fanfictions, Snape could have his own personal vendetta against Dumbledore. Maybe Dumbledore has wronged Snape in the past, and when he sees Harry as a potential victim of Dumbledore's schemes, he decides to help Harry. Another reason could be that Snape has a new understanding of the prophecy and believes that Dumbledore's way of handling it is wrong, so he steps in to help Harry.
Well, it could be for the sake of exploring a different kind of magic or a different set of rules in the wizarding world. Perhaps in this fanfiction's version, the parents were under some sort of dark magic influence that made them turn on Harry. Or it could be a psychological exploration. The writer might be interested in delving into the minds of Harry's parents and seeing what could make them do such a heinous act. It could also be just a very different take on the concept of family and love in the 'Harry Potter' universe.