How does the line “we cling to our last pleasures as the tree clings to its last leaves” impact "The Fly"'s message?

The line about clinging to our pleasures refers to old Mr. Woodifield being allowed out of the house once a week by his wife and daughters to visit his old haunts in London.This seems an innocent pleasure in a privileged life, and we think little of it at first.

Mr. Woodifield goes to visit a younger friend called the boss at his office. Mr. Woodifield mentions that while he was recently in France to see his son Reggie's grave, he also saw the grave of the boss's son, which was quite close by. Mr. Woodifield also notes the vastness of the burial ground and how neatly it is laid out.

Suddenly, the recent carnage of World War I (the story was published in 1922) intrudes. We realize that both Mr. Woodifield and the boss have lost sons in the war, as have many, many people, indicated by the size of the graveyard. We now recognize a somber twist in "clinging to our last pleasures." Mr. Woodifield has had much sorrow in his life due the war.

After Mr. Woodifield leaves, we also become aware of the almost unbearable grief the boss feels over the loss of his beloved only son. His son was the person he lived for and pinned his hopes on. Being reminded of him puts him into a great deal of emotional pain.

The boss then takes his (perverse) pleasure as he can, alleviating his pain by killing a fly with slow drops of ink. He tells the fly to "never say die" and admires its courage and plucky spirit—all the while slowly killing it. In doing so, he reenacts what the world is doing to him, slowly and sadistically killing him, bit by bit.

The story is a commentary on the immense sense of loss and grief people felt after the end of the war and the secret burdens of sorrow they bore. There is not much "pleasure" left in this world to cling to.

Explain the metaphor "we cling to our last pleasures as the tree clings to its last leaves" in 'The Fly'.

The direct context of the quote is that the retired Woodifield, who has had a stroke, is only allowed out to visit the City--central London--once a week by his wife and daughters. They can't imagine what he does there, but then the narrator explains that "we cling to our last pleasures as the tree clings to its last leaves."

A tree clinging to its last leaves is an image of a tree near to death. This statement implies that Woodifield too is nearing death. He is an older man, and it does give him pleasure to get out and visit an old friend, as well as smoke a cigar.

By more than simply a reference to Woodifield, it sets the tone for a very bleak story which primarily concerns death: the death of Woodifield and the boss's sons in World War I (Woodifield has come to report that his daughters saw both graves). It provides a context and becomes a metaphor for the disturbing high point of the story, in which the boss deals with his grief over his dead son by torturing a fly to death, perhaps enacting how he feels he is slowly being tortured to death, drop by drop, by a malevolent god--or how he feels his son died, tortured on the battlefield, drop by drop. In the end, however, the boss does not derive "pleasure" from playing god, for

such a grinding feeling of wretchedness seized him that he felt positively frightened.

Mansfield shows us in this story a life with few pleasures as the older generation grapples with the destruction World War I has wrought.

Strictly speaking, this is a simile, not a metaphor. (Note the use of the word "as" being used for comparison.) What Mansfield means by this is shown in the line immediately after:

"So there sat old Woodifield, smoking a cigar"

Since his stroke, old Woodifield doesn't get out much. In fact, he's only allowed to venture out once a week (on Tuesdays) by his wife and daughters. And as this is a Tuesday, here he is, sitting in the plush, comfortable office of his old friend, the boss. Woodifield's health problems and his enforced captivity at home appear to suggest that he does not have much to look forward to in life. They also hint that Mr. Woodifield has very much entered into his "autumn" years, so to speak. So, by smoking a cigar, he is clinging onto one of the last pleasures he has left in life. In that sense, he is like a tree approaching autumn whose dying leaves are about to fall.