"Truth is absolute" leads to dark places as well. It was the absoluteness of the """immortal science of marxism-leninism""" which gave ideological cover for Stalin's atrocities, and the """application""" of Darwin's theory to the structure of society which gave legitimacy to the ruling classes of the imperial states over their colonies. Saying truth is relative is a statement about the operationality of truth, its status as an aspect of human reasoning, which is fallible, which has no basis in the absolute.

The proposed antidote is exactly the solution supposed by the scientific method: the intersubjective corroboration of individual observations, evidence, reasoning. However, this plainly reveals where truth, science, can fail: It is in this corroboration where atrocities in the name of some transparent, universally available truth are smuggled into society. That is why postmodern thinkers take the footing that they do.

Especially when in the post-war period it was more and more obvious how massive the contradictions were within both liberalism and marxism as they were idealized, and the world as it actually was.

That link gives some context to the tension between postmodernism and relativism. A claim that postmodernism is based on the idea that "truth is relative" is a pretty severe overreach; even the most radical of influential postmodernists are going to be epistemic relativists, not truth relativists (even Derrida was baffled by accusations that he didn't believe in objective truth.)