Why do LEDs not obey Ohm's law?
They do - they just do not have a "fixed" resistance. If you look at it from a standpoint of having a fixed forward voltage drop (which they sort of do - depending on operating region) - look at them more as having a fixed voltage across them. Therefore, as different currents go through them, their voltage will stay (relatively) constant, but the resistance will change.

This is a simplistic answer - but I think you're talking at this level.