Why linear response is absent in a non-centrosymmetric system with time reversal symmetry?

In this paper, it is mentioned that a non-centrosymmetric system with time-reversal symmetry doesn’t have a linear response. It is actually a consequence of the Onsager reciprocal theorem.

But I didn’t understand the theorem properly. Can anyone give an intuitive picture of why the linear response is absent in a non-centrosymmetric system with time-reversal symmetry?