There's something special and that is what you just pointed out. When something is having the same effect whenever it happens, it means there's something special about that event. Bitcoin halving was preprogrammed from the birth of Bitcoin.
It didn't just come from anywhere but was put by satoshi himself because it's special and has great importance. Without the halving, the market wouldn't have had an identity. I don't believe there would had been a four years cycle of Bitcoin. It's the halving that's the mark of the bull market. The halving is what we look up to, the halving makes the circulation of Bitcoin coming into the market to reduce. What this means is that with the same adoption, there'll be lesser amount of Bitcoin available for trading and this increase the price of available Bitcoin.
It's simple demand and supply. There's always demand for Bitcoin so when the supply reduced (in this case just the circulating supply and not total supply) it'll make the price to go up and that's why the halving increase the price. Obviously there are other factors to contribute to this too but we're focusing on just halving for this discussion.