This is kind of a ‘sequel’ from this old question where it ended up as a tangent.
Professor Quirrell spends most of Harry Potter and the Philosopher’s Stone pretending to be a nervous, frightened man who faints at the sight of his own shadow. This is particularly clear in the scene that takes place on Hallowe’en:
Harry was just helping himself to a jacket potato when Professor Quirrell came sprinting into the Hall, his turban askew and terror on his face. Everyone stared as he reached Professor Dumbledore’s chair, slumped against the table and gasped, ‘Troll – in the dungeons – thought you ought to know.’
He then sank to the floor in a dead faint.
Chapter 10: Hallowe’en (p. 127, Bloomsbury paperback)
Towards the end of the school year (and the book), we find out that this is pretense, and that Quirrell himself let the troll in. As he says, talking about the troll that constituted his part in the protective measurements guarding the Stone underneath Hogwarts:
I have a special gift with trolls – you must have seen what I did to the one in the chamber back there?
Chapter 17: The Man with Two Faces (p. 210)
Now, we know that the Stone has been kept at Hogwarts ever since Hagrid took it out of Gringotts before the school year even began, and it seems at least highly likely—though it’s never stated outright—that the protective measurements various teachers provided to keep the Stone secret were placed around the same time.
In other words, we have Professor Quirrell providing Dumbledore with a fully-grown troll as a protective measure some time during August of 1991, managing to both catch it, neutralise it, bring it down into the dungeon-like underground place beneath Hogwarts, and set it up there.
Then, barely two months later, on 31 October (Hallowe’en), we have Professor Quirrell appear in the Great Hall, so scared by the mere presence of a troll in the school dungeons that he actually faints.
Based on Hagrid’s enumeration of which teachers provided protection for the Stone, it seems reasonable to assume that the teachers (at least the ones who helped with the protection) were aware of who did what for the protection. Certainly Dumbledore himself must have been. So at least Dumbledore, and probably at least some of the teachers, already knew that Quirrell had a certain flair for dealing with trolls.
So why did no one seem to find it odd that Quirrell was suddenly fainting at the mere sight of a troll? (Except Snape, of course, but he already suspected Quirrell before this.)
Or, to put the question on its head: Why did they all believe in Quirrell’s jittery act when they knew how he could handle a troll? (Except possibly Snape, if this discrepancy is indeed what led him to suspect Quirrell to begin with.)