I think that people might find symbolism even if the author does not want them to look for it.  Tolkien insisted that The Lord of the Rings was not allegorical.  I guess the question is whether or not authors have a right to say what the book means.

I actually beg to differ. Some would argue that it is impossible to view the world without acknowledging the place of symbolism in it. Whatever the author's intentions, it is possible to look at and examine a piece of literature in a way that the author would never have imagined or dreamed of. Consider the frankly rather sexual analysis of works such as Jane Eyre or Wuthering Heights, which were written by Victorian single women whose knowledge of sex was (we assume) rather limited. Thus, although we must take into account Hemingway's own ideas about his work, we can be free to discount them if we feel we can support our conclusions about his work.

It's always great to read what poets and authors say about their own work.  This quote sounds just like Hemingway, and it's this same no-nonsense approach we find in this novella.  This is just a guy, alone at sea, hungry and wounded, fighting a big fish.  That's it--no symbols or other literary "junk."  It's the simple story of how one man was able to persevere in spite of all those things going against him.  We see him do it and we should be inspired that we'll be able to do the next hard thing that comes our way.

Ernest Hemingway wrote “The Old Man and the Sea” after suffering much criticism from his previous book, “Across the River and Into the Trees”. Hemingway was deeply wounded by the critics and writing "The Old Man and the Sea” was his response to them. However, taking his cue from Mark Twain in “The Adventures of Huckleberry Finn”, he blunted any possible criticism from the critics by saying there was no symbolism in the novella. One hundred years earlier, in a book Hemingway called “the first modern American novel”, Mark Twain did the same thing in “The Adventures of Huckleberry Finn”.

“The Adventures of Huckleberry Finn” begins with the preface, “ PERSONS attempting to find a motive in this narrative will be prosecuted; persons attempting to find a moral in it will be banished; persons attempting to find a plot in it will be shot.

BY ORDER OF THE AUTHOR, 
Per G.G., Chief of Ordnance.

By including a disclaimer in his novel like Twain, Hemingway was insulating himself from those literary critics who had wounded him so deeply after the publication of “Across the River and Into the Trees”. Of course, there is symbolism and allegory in the novel. The fish is obviously his previous novel and the sharks are the literary critics who “ate up” what Hemingway thought was a masterpiece. Hemingway won the Nobel Prize for literature based on this book. It was his way of “defending the title” of the greatest American writer of the 20th century. And, in retrospect, he probably won that title, in spite of his so-called protestations that there is no symbolism.

Hemingway was a straight-forward man. He was masculine and active. He didn't like being clever-clever about literature.

Some books are allegorical. In other words there is a subtext. Even though it is not said, some books use one story to tell another. So you hear lecturers say, "The River" can be interpreted as "The Mind," "The Trees" could be "Fear" or "The Bad Weather" is "Austria's invasion of Serbia," etc. Perhaps the best known allegory is Animal Farm, a story of animals which is actually a retelling of The Russian Revolution.

Hemingway is saying there is no "second layer" in The Old Man and The Sea. The shark is not a symbol for "Death" or "Love" or "War". The old man is not "Time" or "Eveybody". He is just an old fisherman; his simple story is interesting without any interpretation. He is what he is, nothing more.

This quote expresses Hemingway's sense that trying to move below the surface of things, to "add" meaning to things (such as old men, fish, boys and sharks) was not his purpose, but rather what readers have added to his work.  Hemingway didn't want to know what life meant; he just wanted to know how to live in it, how to behave with honor, and thus make your own meaning.  We have in The Old Man and the Sea the struggles of an old man against a shark.  Winning (understanding) is not the end; behaving honorably, both as a fisherman and as a shark, are what determining meaning, and are ends in themselves.  Since life will never make any sense, there's only behavior to judge ourselves by.  (I think there's some hints of Camus here, but I'd have to work that out --- and it's never safe to take what authors say about their works at face value.)