I think that the reality that enveloped Europe after World War I represented on factor that influenced Yeats' writing. Emerging from the war, Yeats and many other thinkers were convinced that the structures and institutions that supposedly provided a sense of totality in the lives of individuals were the same forces that brought on the war, bringing unprecedented death, suffering, and destruction. This is the first stanza of the poem of the images such as "the widening gyre" and the twisted relationship between the "falcon" and "falconer." It is this portion of the poem that makes Yeats mournful for what was endured and the sense of fragmentation, "things fall apart," is an excellent representation of Europe after the First World War.
The second stanza represents Yeats' fears of the future. As bad as the First World War was for Europe, Yeats is convinced that the fragmentation present is going to actually be worse for Europe. It is going to be a situation where some "rough beast" will be born. Yeats was concerned with the overthrow of the Czar in Russia and the Communist government that emerged from it. At the same time, Yeats is almost prophetic in writing about the European fascism that will take a hold of Europe in the 1930s in the form of Mussolini, Stalin, Franco, and, of course, Adolf Hitler. In the second stanza, the fragmented reality of Europe and the lack of any totality is what influences Yeats into constructing a vision of the future that is far worse than the despair of the present.