Why is a rocket almost entirely fuel?

Because a rocket has to carry everything it will ever push away. A rocket moves by expelling part of its mass at high speed, and that pushes the vehicle the opposite way. So the fuel isn't just an energy source: it is also the stuff being thrown. And the fuel you haven't burned yet has to be lifted and accelerated along with everything else.

That is where the trouble starts. The rocket equation, worked out by Konstantin Tsiolkovsky in 1903, says the total change in speed a rocket can achieve (its delta-v) is proportional to the speed of its exhaust, but the mass of rocket you need grows exponentially with the delta-v you want. Ask for a little more speed and you need a lot more fuel, and that extra fuel needs fuel to carry it.

Put numbers on it. Assume an exhaust velocity of 4,500 metres per second, and a trip from Earth to low Earth orbit that needs about 9,700 metres per second of delta-v once gravity and drag are counted. A single-stage rocket would then have to be 88.4% propellant, leaving 11.6% of its launch mass for engines, tanks and payload. Dropping the empty tank partway up helps: in the two-stage version of the same example, 16.7% of the original launch mass is available for engines, tanks and payload. That is why rockets come in stages.

The story behind the equation is human, too. Tsiolkovsky lost his hearing to scarlet fever at nine, was not admitted to elementary schools, and taught himself. In 1911 he wrote that Earth is the cradle of humanity, but one cannot live in a cradle forever. Leaving the cradle, the equation says, is paid for in fuel.