First of this is my opinion and I really do not care if you agree with it or not.

Snape's worst memory: "This will liven you up, Padfoot," said James quietly. "Look who it is..."
"Excellent," he said softly. "Snivellus."
Harry turned to see what Sirius was looking at.
Snape was on his feet again, and was stowing the O.W.L. paper in his bag. As he emerged from the shadows of the bushes and set off across the grass, Sirius and James stood up. Lupin and Wormtail remained sitting: Lupin was still staring down at his book, though his eyes were not moving and a faint frown line had appeared between his eyebrows. Wormtail was looking from Sirius and James to Snape with a look of avid anticipation on his face.
"All right, Snivellus?" said James loudly.
Snape reacted so fast it was as though he had been expecting an attack. Dropping his bag, he plunged his hand inside his robes, and his wand was halfway into the air when James shouted "Expelliarmus!"
Snape's wand flew twelve feet into the air and fell with a little thud in the grass behind him. Sirius let out a bark of laughter. "Impedimenta!" he said, pointing his wand at Snape, who was knocked off his feet, halfway through a dive toward his own fallen wand.
Students all around had turned to watch. Some of them had gotten to their feet and were edging nearer to watch. Some looked apprehensive, others entertained.
Snape lay panting on the ground. James and Sirius advanced on him, wands up, James glancing over his shoulder at the girls at the water's edge as he went. Wormtail was on his feet now, watching hungrily, edging around Lupin to get a clearer view.
"How'd the exam go Snivelly?" said James.
"I was watching him, his nose was touching the parchment," said Sirius viciously. "There'll be great grease marks all over it, they won't be able to read a word." [...]
"Leave him ALONE!"
James and Sirius looked around. James's free hand jumped to his hair again.
It was one of the girls from the lake edge. She had thick dark red hair that fell to her shoulders and startlingly green almond-shaped eyes -- Harry's eyes.
Harry's mother... OotP

We all know that James and Sirius pick on Snape throw out his school year. Just because of Snape's friendship with Lily. Lily has been friends with Snape from the time they meet in that park to there 5th year. Like everyone I feel bad that Snape had a rough childhood his abusive father and The Marauders did not help at all. Like the story goes James gets the girl and Snape becomes biter he holds on to the grudge throw his adult life.

After 11 years Harry comes to Hogwarts when Snape and Harry meet for the first time Harry has the feeling that Snape hates him. This seems true Harry is the son of the man who bullyed Snape. But this did not give Snape the right to bully an innocent child that did not even know of his fathers past.

Snape also took it upon himself to bully all the students that were not in his house. He used his power to bully others.

It does not matter that Snape was really on the good side it does not matter that Snape loved Lily he still a git. Nothing can change that. Snape spend his whole live belittle others when James changed for the better.