Are all volatile liquids combustible?
Many volatile liquids are not combustible

Dichloromethane (DCM) is a widely used solvent by chemists. It boils at around 40°C (the same as diethyl ether) but is not remotely combustible or flammable. Ether is both very volatile and very flammable, so much so that most labs would prefer not to have it used anywhere where flames or sparks could be present. HFC-134a is a refrigerant gas at room temperature and used to be preferred to alternatives like propane (also a gas) because it didn't risk creating an explosive atmosphere when it leaked.

Combustibility has almost noting to do with volatility (other than in the trivial sense that things that are hard to vaporise are hard to set alight even if they are inherently flammable–like bitumen). Combustibility is determined by the chemical properties of a substance, usually whether the reaction of the substance with oxygen releases energy easily. Ether is both volatile and very combustible as that reaction releases a lot of energy and is easy to start. DCM can be burned but releases far less energy and the reaction is very hard to start or maintain as the chlorine in the molecule inhibits the combustion reactions. 

Other compounds, like water, are certainly volatile enough to combust (how would we get rain if water were not volatile?) but there are no possible reactions that release any energy from reacting water with oxygen. 

So two factors matter in combustibility: is there an energy releasing reaction from burning the compound?; is there a reaction mechanism that makes it easy to cause that reaction to happen? Neither are true for water; many other compounds either don't release enough energy from reacting with oxygen or have chemical components that inhibit the reaction.

Volatility has little or nothing to do with either.