The speaker, presumably Yeats himself, is regretting that he is too old to make love! He does not, by any means, disapprove of those who still can and do make love -- "The young in one another's arms" -- although he cannot help thinking that they too -- members of "those dying generations -- are destined to grow old and die. Since he can no longer obtain pleasure and meaning in life from that kind of activity, he is trying to lose himself in his own branch of art, in poetry, as a solace and an escape. When he writes, "That is no country for old men," rather than "This is no country for old men," it indicates that he has already left that other country behind him and is already on his way to Byzantium, which is a metaphor for the world of art and artifice.
One of the most familiar forms of artwork we see in pictures of ancient Byzantium is its mosaics depicting holy men standing in lines, whom Yeats describes as sages standing in God's holy fire / As in the gold mosaic of a wall..." Most of the sages in these mosaics are depicted against a background of brilliant gold mosaic tiles, which to Yeats suggest "God's holy fire." Evidently the poetry Yeats intends to write, including "Sailing to Byzantium," are to be a form of religious worship.
It is possible to escape from worldly cares and lose one's self in artistic creation. This is what Yeats is actually doing and how he plans to spend the rest of eternity. He may be a genius and a great poet, but his feelings are not much different from those of most men when they grow old. They would like to have something to do with their time. They would like to forget about the fact that they will soon have to die. They would like to forget their weak and tired bodies and the wrinkled faces they have to look at in the mirror each morning. They would like to feel that they are still useful to the world and are not just taking up space.
"Sailing to Byzantium" bears a strong resemblance to "Crossing the Bar" by Alfred, Lord Tennyson, written when Tennyson was eighty years old and had only a few more years left to live. "Sailing to Byzantium" was written in 1926, when Yeats was sixty or sixty-one, entering a decade which has been described as "the youth of old age."