The etymology according to Dictionary.com:
gasoline
coined 1865 as gasolene, from gas (q.v.) + chemical suffix -ine/-ene. current spelling is 1871; shortened form gas first recorded Amer.Eng. 1905. Gas station first recorded 1932.
Why was it originally called "gasoline"?
The Oxford English Dictionary writes that there is another step in the etymology--ol:
Etymology: < gas n.1 + -ol suffix (as in benzol n.) + -ene comb. form, -ine suffix1.
The root gas has a meaning which doesn't necessarily mean gaseous in general. It is a specific type of gas. The definition which I think applies here is:
Gas of a kind suitable to be burnt for illuminating or heating purposes; originally = coal-gas n., but now including (a) various artificial mixtures consisting chiefly of carburetted hydrogen, and distinguished by defining words indicating the source from which they are obtained, as water-gas, oil-gas, etc.; and (b) = natural gas n.).
Then, the ol suffix indicated that they were using an oil-based form:
Forming the names of oils and oil-derived compounds (in systematic use in Chem. now replaced by -ole suffix2), as benzol, furfurol, indol (now usually indole), myrrol, pyrrol (now usually pyrrole).
Then the chemical suffix ene or ine was added. So gasoline, when broken down into its parts, perfectly describes what petroleum is: an oil form of a natural gas. The OED writes that the first usage of gasolene was in 1865, and was already being used to refer to what the UK call petrol.
Because it's highly volatile and combustible--and therefore becomes gaseous easily.
edit: Contrary to the charge in the comments that this is "unsupported speculation," there are in fact many examples from the early years of petroleum distillation of the word "gasoline" being defined specifically by its volatility and flammability:
1898: "Gasoline--sometimes, but incorrectly, called naphtha--is one of the lighter products obtained during the distillation of crude petroleum. The nature of the substance is such that it slowly changes to a vapor, or gas, at ordinary temperatures, and if left in an open vessel soon entirely disappears by evaporation."
1878: "The term 'gasoline' shall mean and include all such petroleum as gives off any inflammable vapour at a temperature not less than 73 degrees Fahrenheit."
1870:"The liquids used for producing gas in portable machines are known as Gasoline, Naptha, Benzine, Liquid Gas, Auroral Oil, and by various other names. They are, without exception, highly volatile and, of necessity, inflammable and explosive, and therefore dangerous to the last degree. If they were not they would not make gas."
1865: "As the oil flows from the condenser it is divided into three portions for different uses. The lightest, that comes over first, is called gasolene. This cannot be used in lamps with safety, as it rises in vapor so freely that it mixes with the atmospheric air to form an explosive compound."
1870: "It was proven at the trial that benzine is the product from the distillation of coal oil or petroleum, the most volatile of which is called gasoline..."
1886: "Gasolin is only a trade name to designate a mixture of the various low-boiling petroleum series."
