Summary: Is Snape's vile treatment of Neville only because of Neville's relation to the prophecy? Or does his pride play a role? What is Rowling trying to tell us? A discussion about the relationship between these two characters; what it reveals about Snape's character, and an attempt to answer these questions.
With one word - "Always" - Snape transformed from the despised cynic to the romantic hero of Rowling's absolutely wizard series in the eyes of the Harry Potter fandom. The actions they had once condemned so forcefully were now completely understandable because he was thwarted in love. Hey, we're all suckers for a tear-jerkingly tragic story.
But still, glossing over his treatment of Harry entirely since he was saving Harry's life, although I think making it a misery is a pretty high price - what about the man-who-might-have-remained-a-Death-Eater(had it not been for Lily)'s treatment of the boy-who-might-have-been-the-Chosen-One (had it not been for Harry's blood status)?
My sister pointed out to me that his singling out of Neville for bullying is because of Neville's connection to the prophecy - if Neville's mother had died for her son, Lily would be alive and thriving. I'd stupidly missed that entirely - I'd constructed an entirely different motive, which I still believe is a factor, if a smaller one, in Snape's foul behavior towards Neville. So the question I'm going to address here is: Is the connection between Neville and Snape intentional and if it is, what is Rowling trying to reveal about Snape to readers by this comparison?
Because if you think over it carefully, Snape and Neville led parallel lives in the same way that Voldemort and Harry did.
Let's begin with their family situation. Voldemort and Harry were orphans - Neville and Snape's parents were absent. Well, in Snape's case, he probably wished his parents were absent, because his father was a bitter man who, according to Snape, didn't like anything much. Significant lack of fatherly love here, and because in Deathly Hallows it is clearly said that Snape didn't have an air of being well cared for, we infer that Eileen Prince didn't have much bonding time with her son. The same goes for Neville - his parents had officially lost their marbles and were shut up in a hospital, thereby limiting their quality time with their son. His grandmother is an intimidating personality and Neville's relatives spend most of their time trying to improve him. Poor boy.
So as a result: they both begin Hogwarts with very little self-esteem. I recall reading about Snape's memories in DH and reflecting on how pathetically eager he was conversing with Lily in their first meeting. He was nervous, worried, shy... Neville, too, doesn't exactly ooze confidence. And they both started off at school without too many friends. Snape had Lily, but it had been mentioned that Lily was popular and certainly she wasn't the one brooding over an exam paper on her own after a taxing O.W.L. Excepting Lily, Snape had no real friends - no one aside from her stepped forward to rescue him from James, did they? In the same way, Harry and co. protected Neville from Malfoy (PS, Chapter: Nicholas Flamel, pg. 160). Harry hands Neville the last Chocolate Frog when he's upset after Malfoy cast a full Body-Bind on him. "You're worth twelve of Malfoy," said Harry, "The Sorting Hat chose you for Gryffindor, didn't it? And where's Malfoy? In stinking Slytherin." The difference here is that Snape gave as good as he got; Neville's magic wasn't really up to a high standard.
They both needed friends, while they were not needed by their friends.
In Neville's case this is emphasized when, in their D.A meetings, he is left predictably partnerless when Harry orders them to team up. But the D.A is a turning point for Neville because it increases his self-confidence enormously. He learns to use a wand decently and gains friends, and his standing in Gryffindor house increases. Ditto for Snape, who joins a wannabe Death Eater group. His friend, Mulciber, uses Dark Magic on Mary Macdonald. (Evidently, they, too, are practicing magic, although of a different kind than the D.A.) I'm sure Snape's position in Slytherin becomes better because of this.
And in the end, they both become integral parts of their movements (Snape becomes a Death Eater, even though he switches later) and both become teachers at Hogwarts. Oh, and they both are extremely loyal - passionately loyal - although Snape's fealty is for a dead woman and Neville's is for Harry and Dumbledore.
My point is, briefly, that Snape and Neville have a lot in common, in the same way the Dark Lord and the Chosen One have many similarities. And Harry has noted them - he frets about them. So surely Snape, too, has realized that he and Neville have suffered many of the same unpleasant experiences? Yet while Harry pities Voldemort slightly for this - I distinctly remember him thinking in DH that Voldemort, Snape, and he were the abandoned boys who found a home in Hogwarts. This conveys that he actually sympathizes with the villain who destroyed his life. And in a manner of speaking, Neville destroyed Snape's life - simply by not being the Chosen One. But Snape's too blocked in by his pain and grief to pity Neville. What I'm trying to prove here is that the very human wish to blame someone else, to be so moved to fury at one's enemies that one forgets their troubles, isn't sufficient justification for Snape's cruelty to Neville, because if a seventeen-year-old boy can conquer it...why not him?
And that aside, Snape and Neville have both gone through so much travail. They both have that connection between fellow-sufferers, but Snape ignores it entirely. Instead of taking the boy under his wing, he brutally mocks him - before a new Professor in Prisoner of Azkaban, in front of his classmates in nearly every book, in nearly every Potions class, everywhere, at every opportunity. And why? My answer is this: Snape is proud. We know that - he doesn't want Harry told about his love for Harry's mother, he was enraged when Harry viewed his public humiliation at James' hands in Order of the Phoenix, he boasts to his class in Philosopher's Stone, Chapter: The Potions Master, pg. 102, saying he doubts they'll understand the "beauty of the softly simmering cauldron" and declaring that he is capable of teaching them how to "stopper death"...
And Neville, even his most doting fans must admit, doesn't have the outward appearance of a hero in the earlier books, does he? In the last book he comes into his own, but until then...
I doubt it would have gratified Snape's pride to see himself reincarnated in Neville, who was, besides from being unpopular, useless at Potions. He redeemed himself in Herbology, but Snape would've considered that a soft subject (I can just see his lip curling in contempt at it) because gardening is hardly comparable to learning how to "bottle fame" and "brew glory" (Philosopher's Stone, Chapter: The Potions Master, pg. 102). And Neville's situation must conjure up unpleasant memories that Snape must have tried to bury deeply - memories of a time when he was insignificant, unimportant (which, especially to a Slytherin, must have been horrible).
I think Rowling was trying to prove that a person can move beyond the pain they have suffered in childhood. They say that your experiences shape you, but Neville and Harry did not allow that to happen to them, while Snape and Voldemort did. And there's something else: Harry endeavors to rescue Voldemort right until the end, when he encourages Voldemort to try and feel remorse for his actions, which would save him. Maybe it's common humanity that prompted this, or perhaps its because Voldemort was an orphan like Harry and Harry understands what it feels like to be alone. But neither common humanity or pity and understanding prompted Snape to be kinder to Neville. And that is true greatness: the ability to rise above our own emotions and help someone who has inflicted agony on us.
And hey...just a thought: Snape fans will kill me for this, won't they?
To the well organized mind, death is but the next great adventure.
Dumbledore Sorcerer's Stone
Quidditch started in the 11th century at a place called Queerditch Marsh, which is not marked on muggle maps because wizards have made the place unplottable. Originally it was quite a crude game played on broomsticks with just the quaffle.