One possible reason could be Severus' long - standing grudge against James Potter, Harry's father. Since Severus had a very difficult relationship with James, his hatred might be so deep that it clouds his judgment when it comes to Harry, who is a reminder of James. Another reason could be Severus' loyalty to Voldemort in the past. He might fear that accepting Harry as his son could put him in a difficult position with the Death Eaters or those who still hold onto the old Dark Arts ideology.
Maybe Severus is too set in his ways. He has lived a life full of bitterness and regret. He may not believe that he is worthy of being a father figure to Harry. He might think that he will only bring more harm or misfortune to Harry, so he rejects him. Also, he could be afraid of the emotional vulnerability that comes with accepting a son. Severus has always been guarded and this new relationship might be too much for him to handle.
Perhaps Severus's own self - image is one of solitude and self - loathing. He has spent so much of his life in the shadows, used to being alone and unloved. The idea of having a mate, especially someone like Harry who represents so much hope and light, is so foreign to him that he rejects Harry out of fear of the unknown and a sense of not belonging in a relationship.
Harry might be extremely hurt. He could initially feel a sense of shock and disbelief. After all, he may have started to develop some feelings of trust or kinship towards Severus. Then, he might turn to anger. Anger at being rejected, especially if he doesn't understand the reasons behind it. He could also feel a sense of loss, as if he has been deprived of a chance at a real family connection.
One possible reason could be that he discovers some long - hidden family secrets that make him question his parents' actions or decisions. Maybe he finds out about some dark deeds in their past that he can't overlook.
Well, it could be that Harry has a different view on how to handle the war against Voldemort. Dumbledore is often very strategic and sometimes keeps things from Harry for what he believes is the greater good. But Harry might think that full transparency is necessary. Also, Harry may have formed new alliances or friendships that give him different perspectives, and these new ideas conflict with Dumbledore's. He might feel that Dumbledore's approach is too old - fashioned or risky in a new context.
One possible reason could be that Harry is too focused on his fight against Voldemort and doesn't want to put Ginny in danger. He might think that being with her would make her a target for his enemies.
One possible reason could be Snape's long - standing grudge against James Potter, Harry's father. Since Snape had a difficult past with James, he might project that onto Harry. Another reason could be that Snape is trying to protect Harry in a very strange way. He may think that by rejecting Harry, he is keeping him at a distance from the dangerous wizarding world politics and plots that Snape is often involved in.
Harry might be deeply hurt. He may initially be in denial, not believing that Severus is rejecting him. After all, he may have felt a strong connection. So, he could try to reach out to Severus multiple times, hoping to change his mind.
One reason could be to add a shock factor. It completely changes the expected family relations in the original story. Another reason might be to explore Snape's character more deeply. If Harry is his son, it gives a new perspective on Snape's actions and emotions towards Harry throughout the series.
One possible plotline could be the revelation of the truth about Harry's parentage and how it affects his relationships with other characters. For example, his relationship with Dumbledore might change as he now has a different family connection through Severus. Another could be how Severus deals with having a son all of a sudden and the challenges he faces in protecting Harry in a different way than he did before.
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.