The interviewer asked "why 21 million?" and Tucker stumbled over that one somewhat I thought.
It is basically a result of the period of the reward halving algorithm and the choice for the initial block reward of 50 btc.
After 210,000 blocks 10.5 million btc were created. Now if we half the number being created every 210,000 blocks we will never quite reach exactly twice as many as were created in the first period ...
i.e. 10.5 + 5.25 + 2.625 + 1.3125 + .... = 21
And the general formula for this sum is one of the most well-known summations from mathematics ...
Zeno's dichotomy summationor
... computer guys will enjoy the infinity of base-2 exponents in the denominator, another hat-tip from Satoshi