Well, Snape might heal Draco because of his own sense of morality. Despite his dark exterior, Snape has a code of ethics. Draco is still a student, and Snape may believe that every student should be given the chance to survive and learn from their mistakes. Additionally, Snape could be acting on behalf of Dumbledore in some way. Dumbledore often had complex plans, and Snape was his agent. Healing Draco could be part of a bigger plan to keep the balance in the wizarding world.
Snape may heal Draco simply out of pity. Draco is often in over his head in the dangerous world of the Death Eaters. He's a young boy who is being used by more powerful and evil forces. Snape, having been in difficult situations himself, might recognize this and decide to heal Draco. It could also be that Snape wants to prove to himself that he is not all bad, that he can still do something good, and healing Draco is his way of showing that there is some humanity left in him.
One possible reason could be Snape's long - standing dislike for James Potter, Harry's father. Since Draco is from a pure - blood family like Snape himself, and Snape has a certain affinity for the pure - blood traditions and values, he might choose Draco. Also, Draco was in Slytherin, Snape's own house at Hogwarts, and he might have felt a stronger sense of loyalty to his house and its students.
In some fanfictions, Snape might be trying to gain something from taking care of Draco. For example, he could be using it as a way to get in good with the Malfoy family or to gain some sort of advantage within the Slytherin house politics. However, as the story progresses, his feelings might change from self - serving to genuine care.
In fanfiction, Snape might punish Draco for getting involved with the wrong crowd. For example, if Draco starts to associate with Death Eaters - in - training or those with malicious intentions. Also, if Draco fails to complete his academic tasks or cheats in exams, Snape would surely take action. This is because Snape values knowledge and academic integrity in Hogwarts. Additionally, if Draco causes trouble during important school events or ceremonies, Snape would likely punish him to set an example for other students.
Another motive could be related to his complex relationship with Dumbledore. Dumbledore might have asked Snape to look out for Draco, and Snape, being obedient to Dumbledore in many ways, would do so to fulfill his request. Also, Snape might believe that protecting Draco is part of a bigger plan to maintain the balance in the wizarding world.
In some fanfictions, Snape might use his advanced knowledge of potions to brew a special healing elixir for Harry. He could also use his magic skills, like a complex spell specifically designed to mend Harry's wounds, whether they are physical or emotional.
One reason could be Draco's arrogance. If Draco shows too much pride and disrespect in class, Snape, who values discipline, would not tolerate it. For example, if Draco mocks other students' potions attempts, Snape might punish him.
One reason could be loyalty. Snape is a complex character who has his own loyalties. He might force Draco into situations to test his loyalty to Hogwarts or to the side that Snape believes is right. For example, if there's a threat from Death Eaters in the fanfiction, Snape could force Draco to choose a side, either by directly confronting the Death Eaters or by helping to protect the school.
One possible plot could be that Snape suspects Harry and Draco of being involved in some sort of dangerous or forbidden magic experiment. In his frustration and concern for their safety and the safety of the school, he decides to take a very strict approach. However, this would require a lot of character development and deviation from the original character traits to make it somewhat believable in the context of the Harry Potter universe.
Snape could also use his magical abilities in a more emotional sense. He might share his own past traumas with Harry, creating a bond of understanding that starts to heal Harry's broken spirit. By being vulnerable himself, he shows Harry that it's possible to move past pain.
One interpretation could be a very strict disciplinary approach. Snape was known to be strict, and in fanfiction, this could be an extreme form of him disciplining Draco for some misbehavior in the Hogwarts setting.