The speaker, whom we naturally take to be Yeats himself, wants to escape from his depressing thoughts and feelings about old age. Reality is "no country for old men."
Consume my heart away; sick with desire And fastened to a dying animal It knows not what it is; and gather me Into the artifice of eternity.
It is possible to escape mental anguish through creative work. Alfred, Lord Tennyson's famous poem "In Memoriam A.H.H." is an excellent example. According to the eNotes Summary of that poem:
In Memoriam, unquestionably one of the four greatest elegies of English literature, records the intellectual, emotional, religious, and aesthetic changes Alfred, Lord Tennyson underwent in the sixteen-year period following the early and tragic death of his closest friend, Arthur Henry Hallam, in Vienna, on September 15, 1833.
Tennyson deliberately undertook the task of ridding himself of his grief by composing his long poem over a long period of time. Another famous poem written to get over painful feelings is John Milton's famous "Lycidas," written as an elegy to his classmate Edward King who was drowned at sea. Another of the many poems in this category is Victor Hugo's "A Villequier," written while he was still trying to recover from his grief over the death of his nineteen-year-old daughter by accidental drowning, which had shattered his religious faith. Dylan Thomas's "Do Not Go Gentle Into that Good Night," addressed to his dying father, is another of many examples in poetry. Yet another would be Percy Bysshe Shelley's "Adonais" commemorating the death of John Keats. Then there is Edgar Allan Poe's "Annabel Lee," which obviously applies to the death of his child bride Virginia. Ernest Hemingway once said of himself: "If he wrote it, he could get rid of it. He had gotten rid of many things by writing them."
In "Sailing to Byzantium" Yeats seems to be saying that he feels depressed and even ashamed about growing old. He wants to escape from himself completely by immersing himself in his creative writing, a desire which he symbolizes as sailing to the ancient city of Byzantium, just as Tennyson expressed his depressing thoughts of old age and death in his "Crossing the Bar." Art can serve as a distraction from mental torment. The many technical problems involved in creative self-expression can help the artist to forget the real motive for becoming engaged in the work in the first place.