Here's 3 actual signs of being obsessed with a girl:

1. Stalking her.

2. Refusing to let her go when your friendship with her is over.

3. Wanting her dead because you feel if you can't have her, nobody can.

Did Snape do to or feel any of these things for Lily? Nope.

Here's a little evidence:

If Snape was truly obsessed with Lily, he would've stalked and killed her and her husband James a long time ago.

The only two who were responsible for the death of Lily and James were:

1. Voldemort who actually killed them.

2. Peter Pettigrew who sold them out to Voldemort by telling them about their secret hiding place.

If anything it's Lily's fault that her friendship with Snape ended, not Snape's.

Lily secretly thought it was funny when Snape got s******* assaulted:

She almost laughed when James was humiliating, bullying, and even going as far to remove Snape's trousers (which is a s******* assault).

Snape had every right to call Lily a mudblood. I bet anything he probably saw the twitch in her smile.

So basically if Lily thinks it's funny when Snape gets s******* assaulted, it's fine, but if Snape calls Lily a mudblood after that, then he's the psychopath? That makes no sense.

Lily was a very bad friend to Snape, here's why:

1. She thought it was funny that Snape was getting s******* assaulted by James, so she obviously secretly hated him before their friendship ended.

2. Lily is a hypocrite, she'll think it's okay for Snape to be humiliated, bullied, and sexually assaulted by James, her to call Snape Snivellous, and for Snape to call other muggleborns mudblood, but if Snape calls Lily a mudblood, she'll throw a big old hissy fit and go totally ape.

If anything, Lily is obsessed with hating Snape, because she never got over Snape calling her a mudblood and she refused to forgive him when he felt remorseful and tried to apologize.

If Snape feels remorseful and wants to apologize, then Lily should just hear him out, but nope. Just go ape, Lily. Go ape.

Hermione is far more mature than Lily. Draco called Hermione a mudblood multiple times with a slither of remorse, Hermione might've cried on the first time Draco called her a slur, which is perfectly normal for being called a slur for the first time. But every other time Draco called Hermione a mudblood, she stayed strong and refused to let it get to her, she even forgave Draco by the time they were adults.

As seen here:

Hermione even defended Draco to Ron, twice.

First, she told Ron he doesn't need to fight battles for her, then she says that she, Ron and Draco are all on the same team.

Lily would've never said the same if it were her, James and Snape talking. She'd probably say something like: "Severus, go away! I told you never to speak to me again. Get out before I have you sent to Azkaban."

And this is why Snape was never obsessed with Lily and why Hermione is far mature than Lily will ever be.