Por que Albus Dumbledore colocou o anel de Marvolo Gaunt?

Porque era a Pedra da Ressurreição e significava o "retorno" de sua família. Um meio de liberdade para um Dumbledore mais jovem e um meio de arrependimento para um Dumbledore mais velho. E no momento ele perdeu a cabeça e esqueceu que era uma Horcrux.

'The Resurrection Stone – to [Grindelwald], though I pretended not to know it, it meant an army of Inferi! To me, I confess, it meant the return of my parents, and the lifting of all responsibility from my shoulders.'

[...]

After another short pause, Harry said, ‘You tried to use the Resurrection Stone.’

Dumbledore nodded.

‘When I discovered it, after all those years, buried in the abandoned home of the Gaunts, the Hallow had craved most of all – though in my youth I had wanted it for very different reasons – I lost my head, Harry. I quite forgot that it was now a Horcrux, that the ring was sure to carry a curse. I picked it up, and I put it on, and for a second I imagined that I was about to see Ariana, and my mother, and my father, and to tell them how very, very sorry I was...
_{Deathly Hallows - Chapter 35: King's Cross}

^{(ênfase minha)}

Ele ficou tentado pelo pensamento de ver sua família novamente e ter a chance de se desculpar.

Foi um erro extremamente descuidado e estúpido colocar o anel da Horcrux, especialmente sabendo que era uma Horcrux e o Lorde das Trevas teria colocado uma maldição sobre ele, e depois o próprio Dumbledore admitiu que foi um erro tolo de fazer . No entanto, sua culpa pela morte da irmã e da mãe o levou a esquecer momentaneamente que a Pedra da Ressurreição que o deixaria ver sua família novamente era uma Horcrux, e ele a vestiu.

“After another short pause, Harry said, ‘You tried to use the Resurrection Stone.’

Dumbledore nodded. “When I discovered it, after all those years, buried in the abandoned home of the Gaunts, the Hallow I had craved most of all – though in my youth I had wanted it for very different reasons – I lost my head, Harry. I quite forgot that it was now a Horcrux, that the ring was sure to carry a curse. I picked it up, and I put it on, and for a second I imagined that I was about to see Ariana, and my mother, and my father, and to tell them how very, very sorry I was …” - Harry Potter and the Deathly Hallows, Chapter 35 (King's Cross)

Ele admite para Snape que colocar o anel foi um erro tolo, embora ele não admita a Snape por que ele cometeu o erro de colocá-lo.

“Why,’ said Snape, without preamble, ‘why did you put on that ring? It carries a curse, surely you realised that. Why even touch it?’

Marvolo Gaunt’s ring lay on the desk before Dumbledore. It was cracked; the sword of Gryffindor lay beside it. Dumbledore grimaced.

‘I … was a fool. Sorely tempted …’

‘Tempted by what?’

Dumbledore did not answer.”

Ele tentou interpretar como relacionado ao anel ser uma Horcrux, mas sabemos que isso não é verdade.

“Did you think that breaking the ring would break the curse?’

‘Something like that … I was delirious, no doubt …’ said Dumbledore.”