I think it was because he looked like his father and also Snape thought he was as arrogant as he filthy father! That I hate!
Harry represented what he could have had with Lily, had he not slipped up with her, and Harry also, due to his resemblance to James, kept alive Snape's hatred of James.
Also he may partially blame Harry for Lily's death because if there was no Harry then Voldermort would not have killed Lily.
It could have also been due to Harry reminding him of Lily and that he was responsible for her death.
Dylciara Snape does not necasarily hate him but dislikes him. Probably because his one true love fell for James. Severus was confused because earlier in the years that he's known them both she hated James. And because James treated him badly (shown in OOTP). Harry is James' son so since James died he takes his hatred on Harry. Severus hated James but likes Harry, occasionally.(Only once in PS)