Satoshi may not have stated directly the reason for the halving protocol but the fact is it is quite obvious.
Now when a currency is easy to create it will increase in circulation making it's value drop. Now miners create new Bitcoins by running nodes and solving complex cryptographic math. As they do this they get block rewards which are calculated by hashrates. The bigger the hash rate the bigger the rewards miners get after every successive block they mine.
Now during halving these hash rates are halved which in turn causes the rewards for each mined block to reduce also thus slowing down the rate at which new Bitcoins are created and preventing declination in value due to excess coins in circulation.

If not for the halving protocol the entire Bitcoin supply would have been mined a long time ago completely, making miners to then rely only on rewards from transaction fees.