Well, it's no excuse, but it helps to understand. Somewhere in the books (if I had to guess I'd say in book n°6), Dumbledore explains that Snape is pissed at Harry because of the werewolf prank, especially as James ended up looking as a hero and saving his life. Also he kinda transfered his hate of James on Harry (once again, in book 7, in the memories of Snape you see him and Dumbledore talking, and Snape think Harry is arrogant and stuff (as James was), but Dumbledore says that Harry is closer in looks to James, but to Lili in his mind.
By the way, J K Rowling revealed later that at their time of death, Lily was pregnant and trying to convince James to forgive Snape and make him this next child's godfather.
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