Relativism and strong forms of contextualism assert, from what I gather, that the content of a proposition is not true or false simpliciter, but rather true or false at a time/world/context. A motivation for accepting semantic relativism is the success of possible worlds semantics. It becomes easy to make the move from thinking about possible worlds semantics (specifically, what is true at some possible world) to what is true in the actual world. Quite obviously, there is an underlying assumption here that many find it reasonable to deny: that truthmaker theory of some sort is correct.
If you deny the truthmaker theory for, say, Trenton Merricks’ TSB (truth supervenes on being) account, this slide is wholly illegitimate. Perhaps the truth of a proposition is found in it’s constituent parts or a combination of those parts (the proposition) and not in relation to a possible world. One has a good defeater for analytic relativism if you deny that the truth of a proposition is dependent on a relation to a possible world.