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."