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.
It could also be a test. Snape might want to see how Harry will react under such a menial and demeaning task. He may be secretly observing Harry's character, whether he will complain, try to find a way out, or just quietly do the job. This could be related to some bigger plot in the fanfiction, perhaps Snape is trying to decide if Harry is worthy of a certain task or knowledge later on.
Perhaps Snape is just being his old, bitter self. He may have grudges against Harry for various reasons, like his resemblance to his father. So, making Harry clean his house is just a way for him to take out his frustrations and make Harry's life a bit more miserable, as he often did in the original story.
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 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 Snape's long - held grudges and resentments. He had a complex past with Harry's father, James Potter. Snape might see too much of James in Harry and be unable to separate the two in his mind, leading to his rejection.
Maybe Snape has some sort of premonition or knowledge that Harry is going to be crucial in the fight against dark forces in the future. So, in order to ensure that future, he steps in to save Harry from whatever danger his parents' situation might put him in. He might also be trying to atone for past mistakes or grudges he held against Harry's father by protecting his son.
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.
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.
Maybe Snape is being controlled by some dark magic or a curse that makes him act this way against his normal nature.
One possible reason could be Snape's long - held grudges and resentments. He has a complex history with Harry's father, James Potter. Snape might see too much of James in Harry and be unable to separate the two, thus rejecting Harry despite any potential father - son connection. Another reason could be Snape's own self - loathing and his belief that he is not worthy or fit to be a father figure. He may think that he would only bring harm or a bad influence to Harry's life.
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.
He probably feels angry at first. Harry has always been a bit of a rebel, and being forced to do such a task by Snape, who he doesn't particularly like, would surely make him fume. He might feel it's unfair, especially if he hasn't really done anything wrong.