One of the things that Johnson points out is the belief that the aggression from North Vietnam towards South Vietnam is driven by the Communist leaders in China, and that the same aggression is present in the way that communism has forced aggression on India and in Tibet and previously in Korea. The idea of the Domino Theory was that if one country fell, if the "free world" didn't resist communism that it would eventually spread to envelop the earth in its clutches.
Johnson also suggested in his speech that our commitment there in Vietnam had consequences around the globe. If we didn't uphold our promise of support there, why would anyone in Europe trust the United States? Why would our allies in South America and elsewhere think that we would help them if the specter of communism raised its ugly head there?
And so Johnson appeals to this idea of a logic in which our increasing involvement and the increasing force we bring to bear in Vietnam would somehow lessen the overall possibility of further conflict, that this aggression on our part is necessary to curb further aggression from the forces of communist expansion.