I assume you're asking here about his personal life, rather than the Hallows.

And the answer, in large part, is because he was very ashamed of it.

When Harry and Dumbledore discuss the Hallows, which led to his friendship with Grindelwald and the death of his sister, note how Dumbledore acts.

>'What are you talking about?' asked Harry **startled by Dumbledore's tone, by the sudden tears in his eyes.**
>
>'The Hallows, the Hallows,' murmured Dumbledore. 'A desperate man's dream!'
>
>'But they're real!'
>
>'Real, and dangerous, and a lure for fools,' said Dumbledore. **'And I was such a fool. But you know, don't you? I have no secrets from you any more. You know.'**
>
>[...]
>
>'[...] It was a Cloak the likes of which I had never seen, immensely old, perfect in every respect ... and then your father died, and I had two Hallows at last, all to myself!'
>
>**His tone was unbearably bitter.**
>
>*Harry Potter and the Deathly Hallows* - pp.571-2 - Bloomsbury - Chapter 35, *King's Cross*

And then, listen to how he speaks about the events themselves.

>'Oh yes,' said Dumbledore faintly. **It seemed that he forced himself to meet Harry's eyes. 'You know what happened. You cannot despise me more than I despise myself.'**
>
>'But I don't despise you -'
>
>**'Then you should,' said Dumbledore.** He drew a deep breath. 'You know the secret of my sister's ill-health, what those Muggles did, what she became. You know how my poor father sought revenge and paid the price, died in Azkaban. You know how my mother gave up her own life to care for Ariana.
>
>'I resented it, Harry.'
>
>**Dumbledore stated it baldly, coldly. He was looking, now, over the top of Harry's head, into the distance.**
>
>'I was gifted, I was brilliant, I wanted to escape. I wanted to shine. I wanted glory.
>
>'Do not misunderstand me,' he said, and pain crossed the face so that he looked ancient again. 'I loved them. I loved my parents, I loved my brother and my sister, **but I was selfish, Harry, more selfish than you, who are a remarkably selfless person, could possibly imagine.'**
>
>*Harry Potter and the Deathly Hallows* - p.573 - Bloomsbury - Chapter 35, *King's Cross*

Dumbledore was very ashamed of his past, and you can see here how he can hardy bear to admit his selfishness to one so selfless as Harry.

Recall how he was tortured by visions of these events by the Horcrux Potion in the cave.

Recall how he runs from his past. He does not confront it. He delays meeting Grindelwald, despite death and destruction, to keep his past behind him.

>'You are very kind, Harry. But while I busied myself with the training of young wizards, Grindelwald was raising an army. They say he feared me, and perhaps he did, but less, I think, than I feared him.
>
>'Oh, not death,' said Dumbledore, in answer to Harry's questioning look. 'Not what he could do to me magically. I knew that we were evenly matched, perhaps that I was a shade more skilful. It was the truth I feared. You see, I never knew which of us, in that last, horrific fight, had actually cast the curse that killed my sister. You may call me cowardly: you would be right. Harry, I dreaded beyond all things the knowledge that it had been I who brought about her death, not merely through my arrogance and stupidity, but that I actually struck the blow that snuffed out her life.
>
>'I think he knew it, I think he knew what frightened me. I delayed meeting him until, finally, it would have been too shameful to resist any longer. People were dying and he seemed unstoppable, and I had to do what I could.'
>
>*Harry Potter and the Deathly Hallows* - p.575 - Bloomsbury - Chapter 35, *King's Cross*

But he does not get closure from this, he is still wrapped in self-loathing and shame. He has not made amends for his past.

Secondly, of course, because there are more important things at stake than autobiography.

>'[...] I spend time with Harry because I have things to discuss with him, information I must give him before it is too late.'
>
>*Harry Potter and the Deathly Hallows* - p.549 - Bloomsbury - Chapter 33, *The Prince's Tale*

Regarding the Hallows specifically, of course Dumbledore explains why he didn't tell Harry *that* himself:

>'Harry, I only feared that you would fail as I had failed. I only dreaded that you would make my mistakes. I crave your pardon, Harry.'
>
>*Harry Potter and the Deathly Hallows* - p.571 - Bloomsbury - Chapter 35, *King's Cross*