Why didn’t Húrin answer Morwen as she was dying?

Question

In The Children of Húrin by Tolkien (and edited by his son), Húrin was bound by the power of Morgoth to a stone chair on a high place on Thangorodrim. He is later released after both Niënor and Túrin commit suicide, Niënor by casting herself over Cabed-en-Aras into the river Teiglin, and Túrin falling on his sword Gurthang.

In the final scene of the book, Húrin finds Morwen near the grave of Túrin. She knows she’s dying, and she asks Húrin how Túrin found Niënor, but Húrin doesn’t answer. Why not?

‘Almost,’ she said. ‘I am spent utterly. I shall go with the sun. They are lost.’ She clutched at his cloak. ‘Little time is left,’ she said. ‘If you know, tell me! How did she find him?’

But Húrin did not answer, and he sat beside the stone with Morwen in his arms; and they did not speak again. The sun went down, and Morwen sighed and clasped his hand and was still; and Húrin knew that she had died.

Answer 1

It's possible this is a remnant from an earlier version of the text. In The War of the Jewels, "The Wanderings of Húrin" Christopher explains that originally Húrin didn't come to his wife before her death and she died alone in front of the tombstone, less tormented than Húrin:

It is said by some that Morwen on a time came... to that stone and read it, and died afterwards, though haply she did not understand the tale that it told, and in that was less tormented than Húrin... [Written in the margin later: Some fate of Morwen must be devised. Did Morwen and Húrin meet again?]
_{The War of the Jewels, Part Three: The Wanderings Of Húrin}

It would seem that from the beginning Tolkien felt Morwen should be less tormented than Húrin during her death. However, later Tolkien entertained the idea that Morwen and Húrin may meet.

In a later plot synopsis, Tolkien introduces the idea the Húrin encounters Morwen:

Húrin comes to the Stone and there finds Morwen, who dies.
_ibid.

The conversation at this point has not been fleshed out. However a later manuscript, titled "The Wanderings of Húrin", Tolkien expands on the idea of the conversation between Morwen and Húrin and is near identical to that in The Children of Húrin.

‘Almost,’ she said. ‘I am spent utterly. I shall go with the sun. They are lost.’ She clutched at his cloak. ‘Little time is left,’ she said. ‘If you know, tell me! How did she find him?’

But Húrin did not answer, and he sat beside the stone with Morwen in his arms; and they did not speak again. The sun went down, and Morwen sighed and clasped his hand and was still; and Húrin knew that she had died.
_ibid.

While the conclusions in the comment/other answer may be correct, I find it more likely to be a remnant of the idea from a much earlier writing that Morwen died less tormented than Húrin.

Answer 2

To expand on @Nolimon's excellent comment: You have finally found your long-lost wife but only as she is dying. You're sitting there next to her, having been released from decades of torture, and knowing that your children were both suicides after committing incest. How likely is it you would want your last interaction with your beloved to be one of crushing whatever happiness remains to her?

The text reads:

...Sitting in the shadow of the stone there was a woman, bent over her knees; and as Hurin stood there silent she cast back her tattered hood and lifted her face. Grey she was and old, but suddenly her eyes looked into his, and he knew her; for though they were wild and full of fear, that light still gleamed in them that long ago had earned for her the name Eledhwen, proudest and most beautiful of mortal women in the days of old.

'You come at last,' she said. 'I have waited too long.'

'It was a dark road. I have come as I could,' he answered.

'But you are too late,' said Morwen. 'They are lost.'

'I know it,' he said. 'But you are not.'

But Morwen said 'Almost. I am spent I shall go with the sun. Now little time is left if you know, tell me! How did she find him?'

But Hurin did not answer, and they sat beside the stone, and did not speak again; and when the sun went down Morwen sighed and clasped his hand, and was still; and Hurin knew that she had died. He looked down at her in the twilight and it seemed to him that the lines of grief and cruel hardship were smoothed away. 'She was not conquered,' he said; and he closed her eyes, and sat unmoving beside her as the night drew down.

Unless Morwen knew (or guessed) that you knew the details and demanded them -- and there's no hint of that in the text -- there is simply no reason to tell her for her benefit.

Arguably for Hurin there's the benefit in that he might unload some of his troubles on another, but not only would that be cruel, but by letting her die this way he could at least gain some solace that 'She was not conquered'.