Only thing that's hardcoded is:
1. the initial 50 BTC per block
2. reward halving every 210000 blocks
Just these two factors implicitly determine the 21M limit (or actually: 20999999.9769 BTC).
Yes, but WHY?
The block reward doesn't continue to halve forever. It stops, instead of going to .5, .25, .12, .06, .03, etc.
The correct answer is that Bitcoin was designed to have enough divisible units (Satoshis) to replace the entire money supply of the world. Obviously it was a rough estimate, but the intent was that 21 million * 100 million Satoshis = enough units to replace all fiat money.