Rivalis originally meant belonging to the same brook. Its competitive sense seems to have developed from neighbours sharing access to water. The physical relationship widened into competition for any shared object of desire.
The literal connection to a brook is established; the precise social route to the competitive sense is an interpretation.
Sources
- Merriam-Webster · rival
Dictionary word history; the component and historical references below supply additional detail.
- Online Etymology Dictionary · rival
Historical forms, meanings, and context for the route described here.