The real question is: why 210,000 blocks between halvings? That's the choice that lead to a total of 21 million Bitcoins. Why not a round number of blocks? Say 100,000? Or 314,159 blocks? I guess the reason was to get 4 years between halvings. If that's correct, Satoshi chose 10 minutes between blocks, he chose 50 Bitcoin per block, and he choose to have halvings every 4 years. The 210,000 blocks and 21 million Bitcoin just resulted from this.
I get the feeling that most of the numbers are chosen somewhat arbitrarily. It's probably not so easy to find numbers that are factors of psychologically pleasing numbers (i.e. 2, 3, 4, 10 etc), so the scheme was some kind of arbitrary compromise between simple numbers in places where some rule-of-thumb might be helpful (i.e. the exact number of blocks in 4 years at constant difficulty for halvings), and something "ugly" for aspects that are difficult to maintain whole numbers i.e. the supply cap.
the supply cap is actually a good example to take here: 21 million is in fact a simplification, it's some unwieldy and unmemorable amount *very close* to 21 million, but not 21 million exactly.
really this is classic bike-shedding material: satoshi had to choose something, and it needed to be - 1. arbitrary 2. not too small. we can even bike shed the question in the OP: the question is wrong, you should be asking why satoshi chose to put the decimal point at 8 positions in either direction. Why was satoshi so obsessed with the number 8?
