Severus Snape started out as Harry Potter's bullying, possibly sinister potions teacher in the first novel of the series, Harry Potter and the Sorcerer's Stone. With each subsequent installment in the series, we got to know a little bit more about Snape. By the time the series finished, he had been established as one of the most complex characters in all of fiction, a figure that draws condemnation and admiration in equal measure from across the fandom.
The biggest redeeming feature of Snape's twisted, bitter personality was his uncompromising, one-sided but utterly devoted love for Harry's mother, Lily Potter. But just because Snape was in love with Lily does not mean he would have made a good partner for her, as evidenced by the following points.
Slytherin Vs Gryffindor Rivalry
Snape and Lily knew each other since before coming to Hogwarts. That is when their friendship started. But from the moment they entered Hogwarts, the sorting hat separated the two, putting Lily in Gryffindor and Snape in Slytherin. Now, there is no rule stating two people from different houses can't be together. But just look at the famously antagonistic relationship between Gryffindor's Harry and Slytherin favorite Draco Malfoy.
Slytherin and Gryffindor have traditionally had a great deal of animosity towards each other, precisely because the qualities needed to be in one house are the antithesis of the qualities the other house finds desirable. And their future lives proved Lily and Snape were headed in two very different directions mentally, morally and spiritually.
He Showed Massive Amounts Of Jealousy
Lily was a headstrong, free-spirited person, something that was in stark contrast to Snape's secretive and controlling nature.
In one of the memories that Snape shares with Harry in the final novel, we see Snape and Lily arguing over the amount of time Lily is spending with James and his crew. From the exchange, it becomes clear that Snape is trying to tell Lily who she should hang out with, something that Lily definitely does not appreciate. Snape's jealousy at Lily having any close friends other than himself would surely have only gotten worse with age.
He Hurt Young Petunia
Even Snape and Petunia have something of a history, and not a pleasant one. We now know that it was Snape that Lily used to hang out with when she came back home for the holidays from school. During one such interaction between Lily and Snape, he notices Petunia spying on them, and in response to her typically catty remarks upon being called out, Snape causes a branch to fall and hit Petunia on her head.
It was a small incident, but one that Snape, Petunia and probably Lily remembered, and even though she wasn't sure Snape had done it on purpose, it was the start of Lily realizing there was a darker side to Snape's nature that she needed to be wary of.
He Called Lily A Mudblood
That's right, Snape called Lily a mudblood, the worst possible thing you can call a witch with muggle parents. Granted, Snape said it in the heat of the moment while fighting against James and his entire group of Marauders, but there are no takebacks from something like that.
Even though Snape repeatedly tried to apologize for his mistake afterward, it became clear that it was yet another incident that had done irreparable damage to their friendship.
He Lied To Her
Snape has a long history of lying to people and Lily was no exception. The lies started in school itself when Snape had started to hang out with students in his house who were enamored with Voldemort and dreamed of growing up to become Death Eaters in his service.
Lily found out about Snape's falling in with the wrong crowd, and even though he tried to vehemently deny it, Lily wasn't fooled. It was only the first of many more lies that Snape told Lily and the rest of the world, as he progressed further in his journey towards becoming a servant of the Dark Lord.
He Has An Obsession With Blood Purity
Snape was only a half-blood, meaning he had a muggle father and a witch mother. And yet, he was totally in love with the idea of blood purity in the wizarding bloodline, and the ascendance of Wizards over muggles. Naturally, a consequence of this type of thinking was that Snape looked down upon all those who were not a pure-blooded witch or wizard.
This was in direct opposition to Lily's beliefs. She was a member of the Order of the Pheonix, a resistance created by Dumbledore specifically to act against the spread of Voldemort's ideas and influence. Also, Lily herself came from two muggle parents and had a muggle sister.
He Became A DeathEater
Despite their opposing viewpoints, Snape and Lily managed to remain close friends during school. Their paths started to diverge when Lily started dating Snape's nemesis, James Potter, and Snape himself became more deeply involved with Lucius Malfoy and his gang of cronies who followed Voldermort, who was gaining strength and followers at the time.
The final nail in the coffin was when Snape officially joined the Death Eaters while Lily chose the Order of the Pheonix. There was no longer any question of Lily and Snape getting together once it became clear just how serious Snape was about serving Lord Voldemort.
He Has A Bullying Nature
Snape had a pretty difficult home life, with neglectful parents whom he was ashamed of and wanted to distance himself from as soon as possible. At school, Snape was bullied and ridiculed relentlessly. Then his best friend and love of his life Lily started dating his chief bully James.
All of this affected Snape in the worst way, and he spent a lifetime abusing the power he had to punish those around him, first as a Death Eater and later as a teacher at Hogwarts. The way he belittled, abused and even physically harmed students all the time at Hogwarts earned Harry's hearty dislike and Lily would have had the same reaction.
He Displayed Callous Behavior
When Snape was not being a bully, he was setting new heights for callous behavior on the part of a teacher. When Draco Malfoy cursed Hermione and her teeth grew ridiculously long, Snape's only response was a withering 'I see no difference', causing Hermione to burst into tears and Harry and Ron to curse out Snape together.
It was far from the only time Snape showed indifference towards the suffering of anyone who wasn't himself or Lily. When he first found out that Voldemort was actively looking for Harry with a view of eliminating him, Snape's only concern was for Lily's safety in the event of the Dark Lord coming to her home to murder her infant son.
He Hurt Her Son
The most unforgivable thing that Snape does, at least it would have been in Lily's eyes, is the amount of misery he inflicted on Harry during his time at Hogwarts, simply because he reminded Snape of James. Sure, one could argue that Snape was ultimately protecting Harry, but there is no denying that a lot of what Snape did to Harry would count as physical and mental abuse.
If Lily had been alive, this was probably the thing that would have irreparably destroyed her friendship with Snape and turned her former affection for him into loathing.