If you work out the math, it turns out a solid circular ring around a gravity well, while it can be in equilibrium, it's not in stable equilibrium. It's in unstable equilibrium. This means once it forms it's not going to be staying that way. The slightest tiniest offcenter effect, including the teeny peterbations from other planets in the solar system, will knock it off center and once that happens the orbit will degrade quickly, until one side of the ring gets closer and closer and hits the parent planet.

In order for the orbit of a ring to be a stable orbit, the material that makes up the ring MUST NOT behave like a single solid rigid object. It has to behave like separate particles each in their own individual orbit. Thus a ring of dust or a ring of rocks works, but something like Larry Niven's Ringworld does not.

(This became a major plot point addressed in the second book in the series, where after being told by fans that the Ringworld as he envisioned it wouldn't stay in orbit, The author invented the notion that the ring was artificially stabilized by having been built with ramjet thrusters along the rim that would constantly turn the solar wind into propulsion thrusting back at the sun. So the closer the ring got to the sun the stronger those thrusters would work, pushing back away from the sun, automatically stabalizing what would otherwise be an unstable system.)