Why 21 million coins?
the reason it is 21 and not 20, or 25 or 15 even could be because using round numbers to get close to a 20 million target lands at 21 million:
a block every 10 minutes, 50 btc per block, "halving" every 4 years.
the reason it is 21 million and not 200 million, or 20 billion even might be because a goal was to get bitcoin valued near a dollar within a few years. reaching parity with the dollar was a huge boost for bitcoin, even though, mathematically, it should not have mattered one iota. this is because if you have 10 bitcoins worth $0.10 or one bitcoin worth $1 you hold an identical amount -- they are mathematically equivalent. However we are brainwashed consumers who think something valued at $2 is worth more than something valued at $1.
thus having bitcoin issue a higher number like 500 btc per 10 minutes, for instance, might have made it take a lot longer for the valuation to reach parity with the dollar.
of course, if bitcoin's value reaches hundreds of dollars per bitcoin it might, at that time, be preferable to have more than 50 issued per ten minutes so that each unit of the currency would be more manageable.
but without having had the benefit of the low issuance to begin with, bitcoin might never have caught on in the first place. unless satoshi talks, we'll likely never know.