You’re not comprehending what you’re reading. In that sentence, when it says it modulates the pro-inflammatory and anti-inflammatory response, it’s saying it affects both, It’s not saying that the nervous system itself is pro-inflammatory.

Together, these results uncovered two lines of signalling from the vagal ganglia to the brain. One line (TRPA1) carries anti-inflammatory signals and acts on cNST neurons to enhance the anti-inflammatory response (for example, by positive feedback onto immune cells releasing anti-inflammatory cytokines) and helps to suppress the pro-inflammatory state. The other (CALCA neurons) responds to pro-inflammatory signals and helps to tune down the pro-inflammatory response (for example, by negative feedback onto immune cells releasing pro-inflammatory cytokines).

To “tune down a pro-inflammatory response” and “enhance an anti-inflammatory response” are both anti-inflammatory effects achieved through modulating both anti- and pro- inflammatory responses. Enhance one, diminish another.