Why could no one guess that a Basilisk was the monster?
In the Chamber of Secrets, till the end, no one knows that the monster of Slytherin and the creature behind the attacks is a Basilisk.
<PERSON>, of all people, should have figured it out using the following clues
There are the following observations from which at least <PERSON> could figure out that the creature was a Basilisk:
1. <PERSON> (and <PERSON>, perhaps?) being fond of snakes, it would be hard to miss that the monster of Slytherin would be snake-like at least.
2. There are presumably a limited number of magical creatures that can petrify their victims.
3. The fact that roosters were being found dead in suspicious circumstances was a clue to the Basilisk.
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Plus, it wasn't a satisfactory explanation that an Acromantula killed <PERSON>, as she was uninjured, but dead.
Surely <PERSON> could put two and two together and figure out what the monster was?
I believe the clues pretty much narrow it down to a Basilisk, correct me if I am wrong.
After all, even if it takes​ a genius to figure it out, <PERSON> was the right man for the job!
But he presumably didn't
I say this because:
1. He made no attempt to distribute mirrors among the students as a safety measure.
2. Nor did he station hundreds of roosters in the school to kill the basilisk.(Surely even <PERSON> would have a hard time killing so many roosters quickly to save his basilisk?) This would have been an effective measure, as roosters living as far away as near <PERSON>'s hut were threats to the <PERSON>, so many roosters in the castle would probably get the job done.
Of course these methods are kind of extreme, but they are helpful in saving lives.
My Question
I can understand if no one else could figure out what <PERSON>'s monster was, but why couldn't <PERSON> do so?
After all, all it would take is some digging. <PERSON>, highly intelligent, would probably figure it out easily.
Can someone give me a reasonable explanation for this? 773