Here it is very simply:
A hypothetical spacecraft has total mass of 1000 kg and a main engine that has an effective exhaust velocity of 3 km/s (or 305.915 seconds if you want Specific Impulse in seconds).
Now burn 1 kg of propellant. So speed = 3000*ln(1000/999) = 3.0015 m/s. Kinetic energy = $E_k = \frac12 mv^2$ = 4,499.997 joules.
Later, burn another 1 kg of propellant. So speed = 3.0015 + 3000*ln(999/998) = 6.0060 m/s. Kinetic energy should now be 17,999.988 joules.
...What in the Universe just happened? It spent the same chemical energy both times (1 kg)...but got a much bigger increase in kinetic energy the second time? Where did this much bigger increase in energy come from?
If burning 1 kg of propellant yields 4.5 kilojoules of kinetic energy, then doing the same thing again should yeild another 4.5 kJ, for a total of 9.0 kJ. But no, we get about 18 kJ instead. Where in the world did this extra energy come from?
Dare I ask, are spacecraft perpetual motion machines? Or free energy machines? I don't see how you can put in the same chemical energy and get out very different kinetic energies. Have I done something wrong in my math?