Why does holding my car's RF remote to my head extend its range?

This is just speculation. To confirm any of this would take some careful measurements with fairly sophisticated equipment.

Two things come to mind. First, just raising the remote should help with its range. Try holding it up at chin level but not near your head.

Second, it's possible that the length of your body is roughly resonant at the RF frequecy. By feeding the signal into your body antenna at one end and with the other end loosely coupled to ground your whole body might start acting like a antenna. With the transmitter at waiste level, your body antenna is center fed, which doesn't cause it to resonate as well. Again, this is all just speculation.

I posed this same question to my Electromagnetics professor. His said he would think your skull is acting as a directional reflector and thereby extending the range by focussing more energy to the vehicle.

Another explanation was posted by the New York Times:

The trick turns your head into an antenna, says Tim Pozar, a Silicon Valley radio engineer.

Mr. Pozar explains, “You are capacitively coupling the fob to your head. With all the fluids in your head it ends up being a nice conductor. Not a great one, but it works.” Using your head can extend the key’s wireless range by a few car lengths.