I would say that it's a combination of tradition and game balance. Most people don't wear more than one ring on a hand, and they usually wear it on the ring finger. However, this is not a strict limitation. There are rings for the other fingers and the thumb, and there are rings that are designed such one could place more than one ring on a finger. Consequently, you have a multitude of people who do not adhere to this restriction. But, because the usual fashion norm is only one ring per hand, this is an easy assertion to make.
As far as game balance, this is simply a matter of balancing all powers and items against one another. One could easily redesign any game system such to allow more than 2 rings equipped, however, this would be substantial work to balance all other items and powers against the fact more than 2 rings are allowed. Why go through all that work when the mechanics of just having 2 rings is already known?
There is no actual rule or law imposing the limitation other than what is desired for the structure of the game system. The idea that the magic items interfere is a fiat of the system, not a natural law. One could simply redefine the system without magic items interfering and impose different limitations to obtain the desired overall game balance. However, this leads to what is probably the essential reason: it's easiest to just copy the existing systems which impose the 2 ring limitation because the work and effort to balance the system has already been done under those conditions(game developers are very short on time to really do much innovation).