Why is Slughorn raving about Lily instead of Snape?

[Hagrid]

No: HPFGUIDX 134012

--- "Florentine Maier" <florentinemaie...> wrote:  <snip>
> Florentine:
> I find it ... peculiar that Slughorn ... compares Harry's 
> potions ability to Lily's. Slughorn (was) teaching Snape too, 
> who (was) in the same year as Lily. Wouldn't it make more sense if 
> Harry reminded him of Snape?
> 
> Possible theories...
> a) Snape invented the improved potions ... but passed them on to 
> Lily instead. (Highly, unlikely, since Snape apparently didn't 
> like "mudblood" Lily.)
> b) Lily found out all the potion improvements and practiced them 
in 
> class. Snape copied down everything she did in his book. ...> 

> Sweetpea (cute name) said: Message 133993 <snip>
> <<< ... relationship between Snape and Lily. She
> stuck up for him when James was being a bully to Snape. ...
>  My pet theory is that Snape had a secret crush on Lily 
> and is angry at LV for having killed her. If Dumbledore knew about 
> this ... then this secret might be why Dumbledore trusts
> Snape. >>> 
> 
> <<< 'You have no idea of the remorse Professor Snape felt when he 
> realised how Lord Voldemort had interpreted the prophecy, Harry. I 
> believe it to be the greatest regret of his life and the reason 
> that he returned -'>>>

aussie says:
My 1st posting about this was message 132975:-

Snape, a Slytherin student with ambitions, had call himself a "Half-
Blood"? It is not title you would give yourself to advance your 
position in that house. It seems "HBP" would endear him to muggle 
borns, (ie. Lilly)

The text directions that Harry followed reminded Slughorn of Lilly's
talent. So did Lilly and Snape swap notes on Potions? And what else 
did they exchange?

Remember that JKR was going to include HBP in Harry's 2nd year. I 
suggest similar notes in a 2nd year's book would show a SHIP earlier 
in Lilly's student years before James was an item. Bringing HBP into 
the 2nd last year of a students life at Hogwarts still gives James 
time to make his move on Lilly.

Dumbledore was assured Snape showed REMORSE after he caused the
death of Lilly (and James who he owed a life debt to). Dumbledore
may have double checked his remorse with things we have already
seen. (eg: the pledge the DA members had to sign, or the Unbreakable
Vow)
aussie.