Why do jet engines use kerosene rather than gasoline?
You can persuade a turbine engine to run on just about anything that can burn. So the decision of which fuel to actually use depends on the side factors including, but not limited to:


availability
cost
emissions
hot section temperature
chemical reactions with engine parts


Specific examples:


Coal dust is rather difficult to pump around, and the rampies don't like shovelling
liquid hydrogen (used in the Space Shuttle) requires a lot of storage and has the nasty habit of freezing anything it touches, like rampies.
ethylacetylenedecaborane is unpleasantly toxic (rampies union again) and the combustion byproducts were rather abrasive to the engine's innards
trimethylaluminum would reduce the engine complexity (no igniters needed) because it has the nasty habit of igniting instantly upon contact with air, so leaks are rather dangerous.
natural gas is commonly used as a turbine fuel in pumping stations: it's already there and thus is "free". The required pressure vessels make it impractical to use as an aircraft fuel.


So kerosene basically became the standard turbine fuel because it's:


cheap: kerosene makes up a rather large fraction of crude oil. When you measure your fuel load in tons a few cents per litre makes a difference.
safe to handle: relatively non-toxic, doesn't ignite all that easily
storable and transportable in common structural metals
doesn't clog up the engine