Why do piston engines in aircraft burn fuel at a higher rate than a comparable car engine?
As others have noted, airplane engines and car engines have very different duty cycles.  An airplane engine will typically run at full power for a few minutes during takeoff &amp; climb, then at a large fraction of max during level flight, which may last for hours, and be throttled back only during descent and landing.

An auto engine, by contrast, only operates at full power for a few seconds, as you for instance accelerate up that freeway on-ramp, then it will be throttled back to produce the small fraction of full power that's needed to maintain freeway cruise speeds¹.  Since the power output is proportional to fuel consumed², your car engine uses much less fuel.  Even though it might be rated to produce the same max HP as the airplane engine, in normal operation it produces much lower HP for the vast majority of its operating time.  You can see this in operation if you drive a car with a real-time fuel consumption gauge.  For instance, my Insight hybrid shows ~25 mpg when accelerating or climbing mountains (using near full power), but 75 mpg or better cruising on a level interstate.

Also note that the actual fuel economy of an airplane isn't that much different from say your average SUV.  I don't have the exact figures any more, but I once calculated that my Cherokee 180 got about 18 mpg.  When you figure that it's going twice as fast, and on longer trips can shorten the actual distance travelled by going in a straight line instead of having to follow roads, the comparison isn't that bad.

¹This, incidentially, is why hybrid cars can use electric assist to get much better mpg - the gas engine can be just big enough for efficient cruise, while acceleration is provided by the electric motor.

²To a first approximation.  It's a lot more complicated in the real world.  Look up BSFC maps if you're curious.