At first, Harry might be confused. He may not understand Snape's reasons for not wanting to be his father. As he tries to figure it out, he could become more independent. Realizing that he can't rely on Snape in that way, he might focus more on his own growth and development, relying on his friends and his own inner strength instead of seeking a father - son relationship with Snape.
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 reason could be Snape's deep - seated hatred for James Potter, Harry's father. Since Snape had a very troubled relationship with James during their school days, seeing Harry as his son might be a constant reminder of James, which he doesn't want. Also, Snape has his own life and goals that are perhaps not compatible with being a father figure to Harry. He is deeply involved in the wizarding world's complex politics and his own personal vendettas and loyalties.
He would probably be in shock. Snape has spent so much time around Harry in one way or another throughout his years at Hogwarts. His immediate reaction could be disbelief. He might stand there frozen for a moment, unable to process what he's seeing. Then, the full weight of the situation would hit him, and he could break down in a rare display of raw emotion.
In some fanfictions, Snape might awkwardly try to comfort Harry. Given his own complex personality, it wouldn't be an easy or natural gesture for him. He might pat Harry's shoulder stiffly or offer some gruff words of reassurance like 'Pull yourself together, Potter.'
Snape might be initially shocked. He has his own preconceived notions about Harry, and this revelation could completely change his view. He might struggle to accept it at first, given his traditional and somewhat rigid personality.
He may also get angry. Harry has a strong sense of justice and self - worth. Snape's rejection could be seen as unfair in his eyes, especially if he has started to develop some sort of positive feelings towards Snape. So, he might lash out at Snape or even try to prove him wrong by becoming more independent and successful on his own.
Snape could initially be skeptical. Given their long - standing enmity, he might not believe that Harry's apology is sincere at first. He might respond with a cold glare or a sarcastic comment, like 'Potter, your apologies are as empty as your head.'
Harry could react with anger. He is a strong - willed character. So, he might confront Snape about his hatred. He would demand to know why Snape is treating him this way when they should have a father - son relationship. This could lead to a series of intense arguments between them.
Harry might be initially shocked and embarrassed. A Howler is a very public form of scolding, and in front of all his friends and classmates, it would be a humiliating experience for him.
Snape's reaction could be quite mixed. On one hand, he might be angry at Dumbledore for not doing more if he knew about the abuse. He may also feel a strange sort of empathy towards Harry. After all, Snape himself had a difficult childhood. So, he could start to be a bit more lenient with Harry in his classes and try to subtly offer support.