Answer:
Based on the context of the statement, President Lyndon B. Johnson's primary reason for his announcement was the United States' involvement in the Vietnam War.
In the statement, President Johnson mentions that America's sons are "in the fields far away," which suggests that he is referring to soldiers fighting in a war. He also mentions that "our hopes and the world's hopes for peace" are at stake, which suggests that he is concerned about the consequences of continuing to engage in conflict.
Additionally, the statement was made in March 1968, which was at the height of the Vietnam War. It was a time of intense public opposition to the war, with widespread protests and demonstrations taking place across the country.
Therefore, it is likely that President Johnson's primary reason for his announcement was the United States' involvement in the Vietnam War, and his decision not to seek re-election was motivated by a desire to focus on addressing the challenges and responsibilities of his office, including finding a resolution to the conflict.