How is oil-filled switchgear possible?
There are a few things you seem confused about.

First, if you have a arc that generates a pocket of oil-vapor that is submerged in a pool of liquid oil, it can never ignite, as there is no oxygen there.

With regard to quenching, basically the idea is to "stretch" the path of the arc until it breaks, and is as such quenched. There are actually high-power circuit breakers that specifically force a jet of air through the arc path when they open to quench the arc as rapidly as possible.

Basically, the liquid is supposed to boil, as this provides a source of gas. Also, it's worth remembering that the phase-change from liquid to gas requires a lot of energy, and this helps absorb the heat generated from the arc.

It is true that if a oil-immersed breaker cycles often, it will use up most of the oil, both through vaporization and carbonization, but the device should have sufficient oil to last for it's rated cycle-life.