harry potter - What makes the Whomping Willow so valuable to Snape?

At the start of Harry's second year, Harry and Ron arrived at Hogwarts in a flying Ford Anglia which crashed into the Whomping Willow.

Snape had several objections to this theatric arrival, his main one being that the boys damaged the tree:

"I noticed, in my search of the park, that considerable damage seems to have been done to a very valuable Whomping Willow,” Snape went on. “That tree did more damage to us than we—” Ron blurted out. “Silence!” snapped Snape again. _{~Harry Potter and the Chamber of Secrets - Chapter 5: The Whomping Willow (emphasis mine)}

The tree originally was put there to trap a student while he was in werewolf form. There is a better solution now, a potion called Wolfsbane, so the tree probably serves no purpose except occasionally whacking some first-years who wander too close, ignorant of its existence. Snape couldn't have seriously thought that damaging the tree would cause Dumbledore to expel Harry Potter, the boy wonder, the one Snape was tasked to protect.

“Well, you’re expelling us, aren’t you?” said Ron. Harry looked quickly at Dumbledore. “Not today, Mr. Weasley,” said Dumbledore. “But I must impress upon both of you the seriousness of what you have done.
"..."
Snape looked as though Christmas had been canceled. He cleared his throat and said, “Professor Dumbledore, these boys have flouted the Decree for the Restriction of Underage Wizardry, caused serious damage to an old and valuable tree — surely acts of this nature —”
_{~ibid (emphasis mine)}

Strangely enough, Snape seems to think that these two offenses put together are severe enough to compel Dumbledore to actually expel Harry and seems disappointed that it is not so. Why is that?

One would think that the location where he was almost mauled to death by a werewolf wouldn't be so precious to Snape. The tree is a relatively new arrival, there are no long-standing Hogwarts traditions and stories about it, except Lupin's, so what makes the Whomping Willow so valuable? Was it a dig, aimed at Dumbledore for bringing dangerous things (werewolves and brutal trees) into Hogwarts?

Answer

Snape almost certainly didn't personally or emotionally value the Whomping Willow. He certainly wouldn't have positive associations with the place he was nearly attacked by a werewolf.

However, there are two things to consider. The first is, as a professor, Snape would have some idea of the "objective" value of school property even if he personally has negative associations with it. Him saying it's valuable could be referring to its objective value, not to its value to him. The second thing is, he wanted Harry and Ron to get some sort of punishment for what they did, and probably figured Dumbledore wouldn't be inclined to punish Harry. He didn't want them to get off lightly for flying the car to Hogwarts, so he made sure to emphasize all the reasons it was wrong.

The first time the mentions its value, it's in telling Harry and Ron what they did wrong, and making sure they know they're in BIG trouble.

“I noticed, in my search of the park, that considerable damage seems to have been done to a very valuable Whomping Willow,’ Snape went on.

‘That tree did more damage to us than we –’ Ron blurted out.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 5 (The Whomping Willow)}}

The second time he mentions how valuable the tree is, it's right after Snape finds out that Dumbledore isn't going to expel them (and probably suspects they'll get away with a very small punishment if any).

He likely didn't want them to be actually expelled, since he was loyal to Dumbledore, but he certainly did want them to be punished.

“Snape looked as though Christmas had been cancelled. He cleared his throat and said, ‘Professor Dumbledore, these boys have flouted the Decree for the Restriction of Underage Wizardry, caused serious damage to an old and valuable tree … surely acts of this nature …’

‘It will be for Professor McGonagall to decide on these boys’ punishments, Severus,’ said Dumbledore calmly. ‘They are in her house and are therefore her responsibility.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 5 (The Whomping Willow)}}

It isn't really clear how rare Whomping Willows as a species are. The only indication is that Lockhart says his experience with exotic plants would make him good at tending to the Whomping Willow - but Lockhart is a liar and could have been saying he's met exotic plants to make himself seem more impressive, so that doesn't necessarily mean much. However, no Whomping Willow is mentioned other than the one at Hogwarts, so it's possible that they might be rare.

In addition, "valuable" might be used somewhat in reverse - not referring to the tree itself, but referring to how costly, time-consuming, or dangerous tending to its injuries might be.

“Professor Sprout’s arms were full of bandages, and with another twinge of guilt, Harry spotted the Whomping Willow in the distance, several of its branches now in slings.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 6 (Gilderoy Lockhart)}}