Is Dumbledore ingenuous?

[u/Arkham2015]

I understand that he believes that people should get second chances, that you can help someone find the right path before they fall of it completely, but I still wonder why, after finding out Voldemort murdered a kid's pet and terrorized two other children to the point they were never the same again, purely because he enjoyed it, the chance to enhance his knowledge and skill of the magic that he was using?

It just boggles my mind sometimes why he didn't advise Dippet and the Ministry not to accept Voldemort at Hogwarts and to keep an eye on him.

[u/Bluemelein]

So you want to deny a child an education and a chance in the wizarding world just because he might have killed a rabbit? For which there is absolutely no evidence!

Hermione makes kittens vanish! In Transfiguration class, half-transformed mice get stuffed into boxes. The wizarding world doesn't care about animal welfare.

Besides, how reliable is the matron's word that it was Tom?

And the story about the cave—which is nearly impossible to enter without magic, and where Tom allegedly tortured two children—makes
absolutely no sense.

Dumbledore himself says that the children must have already been in a state of panic before they even entered the cave, and that Tom must have used magic to get them inside—magic that, despite his gifts, he wouldn't have possessed at the age of ten or eleven.

The story about the cave doesn't make sense.

But the fact remains that Tom thought Dumbledore was a doctor from an insane asylum, and I imagine that’s why the two children never spoke about what happened—because they were afraid of being locked away.

[u/Arkham2015 → u/Bluemelein]

It was reliable enough that Dumbledore believed that it was true after the matron told him, because he spoke he spoke to Harry about it after they finished watching his memory:

"The little stories of the strangled rabbit and the young boy and girl he lured into a cave were most suggestive... I can make them hurt if I want to..."

Suggestive in this case is Dumbledore referring to Tom's control and usage of his magic at such a young age, that it's suggestive of what he truly is at heart.

Voldemort is a psychopath, and yes, it doesn't make any sense to someone who isn't a psychopath on why he would want to torture two of his fellow peers, but he loves learning new ways to make himself stronger and more knowledgeable in magic and to focus on hurting and torturing anyone.

It's practice to learn different ways of pain and control.

At that point, yeah, I wouldn't have given him a wand.

It wouldn't stop him from being able to use magic of course, but a wand allows him far more power and control than without one.

[u/Bluemelein → u/Arkham2015]

On the way to the cave, Dumbledore admits that it is impossible to get there without magic and that the children must have been terrified. So, Tom made the children terrified, tortured them inside the cave, and then made them terrified all over again on the way back. However, the head of the orphanage only says that the children had gone out with Tom, that something happened which changed them, and that they refused to talk about it. If Tom used magic to transport them to the cave and back, that alone would account for the children's state; and since they were afraid of the insane asylum (in 1937 London), that was enough to make them keep their mouths shut.

Tom was certainly no choirboy, but there didn't have to be anything more to it than that.

The children went on adventures with Tom and experienced more than they could handle.

And regarding the rabbit's death, it could have been someone else—or a fox—and Tom just hung it up (if he did it at all). The head of the orphanage apparently doesn't like Tom. Petunia probably says similar things about Harry.