In the Philosopher's Stone, Harry, Hermione, Neville and Draco are punished and have to assist Hagrid in his search for a dying unicorn.

Malfoy mentions that according to rumors, there are werewolves in the Forbidden Forest. When they ask if a werewolf could kill a unicorn, Hagrid answers that they are not fast enough to do that. He does not answer, "There are no werewolves in the forest", which is evidence that there are indeed werewolves (since Hagrid knows the ins and outs of the Forest as we are told).

Now from what we learn in The Prisoner of Azkaban, werewolves are humans that were bitten by other werewolves; they transform into werewolves during a full moon.

Does the information we get on werewolves in book 3 contradict what we can infer from book 1?

In particular:

• Why would Hagrid not refute the idea of werewolves attacking unicorns simply using the fact that they transform once per month, and that Hagrid found two different unicorns attacked in a week (instead of using a dubious speed argument)?

• Why would werewolves stay in the Forbidden Forest all year, when we know werewolves are actually human people who, although they are often rejected by normal wizards, would probably not be ignored by Hagrid and especially by Dumbledore, who I can't imagine would not offer any help to infected people staying in the forest near his school.

• Why would they even let werewolves occupy the forest if one bite on a student could kill him or infect him for life? Sure it's the "Forbidden" Forest but, assuming there were werewolves as described in book 3 in it, the werewolves would probably drastically decrease the security of students.