The story
From para- (“beside, adjacent to”) + sympathetic, because some of these nerves run alongside sympathetic nerves.
Etymology from Wiktionary, CC BY-SA 4.0.
parasympathetic
Today it means: Of or relating to the part of the autonomic nervous system that inhibits or opposes the effects of the sympathetic nervous system. It consists of nerves arising from the brain and the lower end of the spinal cord and supplying the internal organs, blood vessels, and glands. Full definition →