Some airplanes (like the 737 with it's three-step RTO manuever) have a disadvantage when it comes to handling the RTO from the RHS, so it makes sense that the captain will perform the RTO.
Typically the captain will be the most experienced pilot on the flight deck and (typically) the person to make the best judged decision to perform an RTO or not. Unlike a go-around, an RTO is not always the safest option and can easily lead to the aircraft going to the valley beyond the end of the runway in some scenarios, even when rejecting well below V1. You'd want the most experienced person performing that decision whether to reject or not, based on the input from the FO side as well, of course.