Follow the money. The big picture money.
The bond market is bigger than the stock market.
Because of that, any movement of money into or away from bonds will be magnified in the stock market. When interest rates drop, new bonds yield less than before*. In that case, big money moves from the bond market to the stock market. Here is one snapshot of the bond market today.
View attachment 129091
* Any bond bought and held to maturity is unaffected, they still pay the profit as prescribed. The long-term value is unchanged. However, for many players who buy and sell bonds repeatedly instead of holding to maturity, the instantaneous temporary value of the bond drastically changes with interest rates. As interest rates drop, the bonds that pay higher interest rates have their instantaneous value go up (and the reverse when interest rates rise). Bonds can gain/lose money, temporarily, if you don't hold to maturity.