Snape seems to hate "Potter's Gang" irrationally, even if Harry reminds him of how he lost Lily. "Potter's Gang" is comprised of four people: Harry, Ronnie, Neville and Hermione. The Marauders, who often bullied Snape, were four: James, Sirius, Peter and Lupin, and their leader, James, went on to marry Lily. Of course the parallels would be brought even closer for him.
It goes further than that, since each member of Potter's Gang is similar, on a superficial level, to one of the Marauders despite two being girls (and despite Snape not looking past these traits due to his bitterness) - Harry is like James, Ronnie is rather like Sirius in being his best mate, Hermione is bookish and sensitive like Remus, and Neville is a lot like Peter (if braver within and far less likely to turn traitor as a result). Hagrid is actually alluding to this very fact when he brings up the Marauders, and how badly they interacted with Snape.