I suspect that Satoshi started with an initial per-block reward of 50 BTC which cuts in half every 4 years (210,000 blocks). The consequence was 21 million coins over time.
210,000 is an equally strange number, other than being exactly 1% of 21 million.
210,000 comes from 10 minutes, 4 years, and 50BTC/block. Those are a little less strange imo. Only the block award is arbitrary, but 50 feels nice to me.
edit: arbitrary is the wrong word. I mean that 10 minutes can be chosen for a reason and so can 4 years.