Satoshi simply backed into it. 1 sat for each block of the final epoch (halving period), 2 sats for the blocks of the 2nd to last epoch, so on and so forth all the way back to the first epoch (50 ₿ per block).

This gets you exactly 20,999,999.97690000 bitcoins. Believe it or not, this is the ACTUAL total maximum supply of bitcoin - not 21,000,000.0000000, as many commonly believe. It is simply rounded to 21M ₿.

Now that you understand that 21M ₿ was fairly arbitrary, in that it was likely "backed into" by nature of this halving schedule, you can probably understand why 210,000 blocks was the duration chosen to regulate the issuance. It simply gives us a fairly round number of roughly 21M coins... instead of something like 20,638,011.94747192 coins.