The meaning of the proverb is that only Nixon could have gone to China, given his distinctively hawkish and conservative stance on Sino-American relations during his ascent to power. Nixon was widely viewed to be a leading (albeit somewhat restrained) voice in the country’s struggle against communism.
And the converse, oft-overlooked in international discourses, equally holds true. Only Chairman Mao Zedong – with his consolidated presence as the supreme leader of Chinese politics – could have had the political resolve and wherewithal to push back against the strong undercurrents of the then-raging Chinese Cultural Revolution to forge ties with the United States.