It's not quite as arbitrary as it seems...
The final total of the infinite series is twice the number issued in the first 4 years (before the first halving). That, in turn, is determined completely by the initial block reward (and the 10 min block time).

So once satoshi had decided on the mechanism and issuance rate, the only parameter left to play with was the initial block reward of 50 btc.

Total of 1 btc would mean there's only 10^8 units (satoshis) to handle the whole system ... not enough.

50 per block probably seemed like a good number to get them mined, distributed, enough to play with even if one only mined one block, etc.

I'm guessing about it tho...someone correct me if i'm missing a good reason here.