I am very new to this idea. My only knowledge of it is from the wikipedia page.
It seems odd to me that there is an upper limit at all to the bitcoins that will be issued. Perhaps there is a simple explanation to this. Why was that limit set at 21 million?
There are a lot of reasons and I don't think it's known what factors led to the final decision.
For one thing, when the basic Bitcoin mechanics were designed, there was a significant risk that Bitcoin would never be adopted. By giving a fixed term to mining and a fixed supply of Bitcoins, the original designer(s) increased the chances that people would want to acquire Bitcoins. The prospect that future scarcity would increase their value likely induced people to mine even when the economic argument for doing so was quite thin.
It's also possible that there was hope that people who didn't like inflationary currencies would be drawn to Bitcoin. There are people who see inflation as a theft or tax. The ultimate lack of inflation in Bitcoin attracted people with those views to the currency.
And, of course, some way was needed to distribute the currency. Using the initial distribution of the currency as a way to build sufficient computing power to use proof of work to secure the currency until transaction fees could take over was probably Bitcoin's biggest bit of genius.
It appears this strategy worked, at least so far.
Short answer (and just my opinion):
The total number of bitcoins issued needed to be a low enough number so that while total dollar valuation of all bitcoins combined was still in the single-digit millions the exchange rate would reach parity with the U.S. dollar at some point.
Why that matters?
Because people don't know how valuations work.
They don't know that a $100 worth of shares of Blackberry (BBRY) at $13.54 each is probably better to own than a $100 worth of shares of Best Buy (BBY) at $24.11. Just because one has a higher "price" (exchange rate) doesn't mean it is preferable to own.
So because a Bitcoin was worth more than a dollar early on, that helped it gain a bit of "legitimacy" and recognition.
I find this surmise by Cryddit on BitcoinTalk interesting:
Satoshi cared that people using Javascript (?) or other languages which encode all numbers as 'double' (64-bit floats) would not have to jump through hoops to avoid stupid accounting mistakes.
Your 64-bit float has 52 bits of mantissa, so, in order to avoid rounding errors ever going the wrong way, the number of units involved in bitcoin-related math must never be more than 251, which is 2251799813685248 units. 21 million coins times 108 divisions (Satoshis as they are now called) is 2100000000000000 units - comfortably just below the limit allowing "simple" accounting implementations in such languages to be accurate.
And as Hal Finney pointed out in 2008, even if the entire M1 money supply of the world as of that time were expressed in Bitcoins, the smallest division would still be worth less than 1 USAmerican penny, so there is no need for more than that many units.
