I think it largely comes from uninterrogated/unrevised dualisms applied to the scientistic world. I think of Rosenberg's eliminativism as follows:

a) Platonic realism is the only way our semantic categories/abstractions could be meaningful.

b) The world is physical (platonism is not true).

c) All our categories are meaningless! Our abstractions are unreal!

You can see it all follows from a), and there are serious questions about whether this is actually a physicalist philosophy...