There is not really a metaphor for fish in the short story "Big Two-Hearted River" by Ernest Hemingway. The fish in the river are literally present, and Nick's fishing constitutes the main arc of the story. Instead, as discussed above in other answers, the fish stand as a metaphor for the state of Nick's inner self. To understand this distinction, it helps to discuss the nature of metaphor.
A metaphor is defined as an implicit comparison not using such explicit comparative words as "like" or "as." Explicit comparisons, such as Robert Burns' "My love is like a red, red rose," are called similes. A metaphor, though, is more subtle, such as John Donne's line "Till age snow white hairs on thee." In this line, snow is being compared to old age, in that it makes hair white. This leads us to the two major parts of the metaphor:
- Vehicle: The vehicle is used to convey the central idea of the metaphor. In the line by Donne, the snow is the vehicle, used to illustrate the poet's idea of aging. Snow here is a concrete image being used to illustrate something more abstract. In Hemingway, the fish is the vehicle.
- Tenor: This is the point of the metaphor, in Donne the nature of old age and the passage of time. In Hemingway's story the tenor is Nick's psyche.
In Hemingway's story, the fish and the fishing trip itself are the vehicles that the author uses to describe Nick's gradual healing from the trauma of war. Nick's internal psychological state, and the psychological wounds of war he bears (what we might now call PTSD), are the tenor of the metaphor.
The successively better fish Nick catches serve as metaphors for how Nick himself gradually recovers from his war time experiences by reconnecting with the natural world. Thus we would describe the fish as metaphors for Nick, rather than talking about metaphorical fish, for the fish are, in fact, literally present in the story.
According to Burton Raffel, author of How to Read a Poem, metaphor is
A frame of mind, a way of looking out from an inner world of essentially personal thoughts and feelings
This "frame of mind," then, effects an unstated comparison between two unlike things. In "Big Two Hearted River, Part 2" Nick Adams has come home from war damaged by its horrors, so he returns to the woods and the river where in the regenerative setting of nature, a place where he learned of the world as a boy, he may experience nature's restorative properties. Having spent the night in a tent, Nick cooks a breakfast when he finishes catching grasshoppers for bait. Afterwards, he goes to the river, and stepping into its cleansing water, he takes out his fly rod and begins to fish in a place that is at peace and right with nature.
In the inner world of metaphor, the fish may be comparable to the soul of Nick. One large trout is hooked, but he is able to break free, although he is damaged. Likewise, in the war Nick has suffered tragedy, but breaks free to the river. Another is too small, and Nick releases it, careful to not scar it when he touches it to be sure it can move all right. This small fish may be comparable to Nick's heart, scarred but whole. After Nick catches "one good trout," he is satisfied; "[H]e did not care about getting many trout" having been healed sufficiently by nature to be content. He walks along the river, which is always symbolic of a journey, but "[H]e did not want to go down the stream any further today."
....Nick did not want to go in there now. He felt a reaction against deep wading with the water deepening up under his armpits, to hook big trout in places impossible to land them.
Nick is not fully healed, but he can return to the Big Hearted River that will again receive him:"There were plenty of days coming when he could fish the swamp." Nick will eventually return to society and its complications.
The act of fishing is Nick's way of trying to heal his "scars" from the war.
- A metaphor for the fish is the soul and the heart of Nick.
The small fish that he catches and releases is comparable to soul; that is, his inner self and conscientiousness that wrestle with the impaling hook of war which has injured him. When Nick puts the fish back into the water, the water, which is always symbolic of cleansing, acts to clean away the wounds of war. Nick is careful to wet his hand before touching the fish so as not to leave that "white mark" he describes that can lead to death. The fish is re-baptized in the water and moves, living anew, just as Nick will live anew.
As is also mentioned above, the small fish may be comparable to Nick's heart, that is restored as he fishes and camps out in nature. like the wounded fish, too, Nick is scarred by war. But, he, too, will heal and return to society as the fish returns to the waters of the river.