After halving, the supply of Bitcoin been mined also get reduced and that means a lesser amount of Bitcoin coming into the market and there's less bitcoin circulating. Don't forget some bitcoin that are been lost as some individuals died without any heir to their investment.
The less money is unearthed at a day, means that day must be a lot easier to move higher and that is why most of the time after halvings are done, the price starts to go up. It takes a while because there could be saved some aside, but when those are done, the price starts to go up because otherwise miners do not make a profit and when they do not sell, the price starts to keep growing more and more.