I've assumed it's because a larger body, with more cells, needs more neurons to monitor and model it, but it's not compelling.

The "law" is mere empirical correlation - e.g. you are smarter than a blue whale.

The fantasy that the baby spiders with encephalization quotients (https://wikipedia.org/wiki/Encephalization_quotient) off the charts (because their brains displace their digestive systems and partly fill their legs) are more intelligent than humans, appeals to me. I suspect raw intelligence doesn't require many neurons. But spiders aren't social.

Parrots are.