Basilisk

A basilisk is a monster with a rule: look it in the eye and you do not walk away. Indirect sight is a lesser harm, which is how the mystery can last a school year without emptying the castle. The creature is old, housed under the school, and tied to a founder’s worst idea about who should be allowed to study there.

This is the fact of the animal, not a retelling of the descent. Spiders fear it. Roosters are its old enemy in the legend the book uses. Both details are canon, and both are more interesting as clues than as trivia stamps.