There appears to be no specific reason why Satoshi chose to give a 50BTC reward as a starting point and divide it by two on every block halving.
According to some Google quotes, that is Satoshi's best guess for rewarding early participants and adopters, even though it has no value.
It seems that Satoshi thinks about the "Gold Analogy" and applies it to BTC. Look at the Bitcoin.pdf part quoted below
The steady addition of a constant of amount of new coins is analogous to gold miners expending
resources to add gold to circulation. In our case, it is CPU time and electricity that is expended.
Source: https://bitcoin.org/bitcoin.pdfI got this quoted below from reddit here
https://www.reddit.com/r/Bitcoin/comments/m14sir/anyone_who_owns_21_bitcoins_is_a_millionaire_today/“I wanted to choose something that would make prices similar to existing currencies, but not knowing the future, it is very difficult. I ended up choosing something in between”, Nakamoto said in an email to Hearn.
Based on what I understand, it appears that all of them are just guesses, with no specific reason why he began with 50BTC as a reward and then halved it every 210,000 blocks.
But his purpose, as we can tell, is to grow its value and fairly distribute the reward, which is exactly what we are seeing right now.
And the 50 BTC reward is to encourage participants to participate and help the network be more secure.
And block halving to tighten the reward, with each block halving reducing supply and driving up the price.