Look at the formula for discounted cash flow. It's a widely used valuation model and applies to lots of companies, especially those in the growth phase where current market cap is largely dependent on expected cash flow far into the future.

https://en.wikipedia.org/wiki/Discounted_cash_flow

Notice the denominator in the series - (1+r)^n where r = interest rates and n = number of years out. The more r rises, the more terms at the end of the series drop out because they're so close to zero. So that effectively means a company that's getting its value from cash flow 10+ years from now loses a lot of its value if interest rates are rising.

Because investment in stocks competes with investment in government bonds. At just 1% increase in bond interest, trillions of investment dollar will flow from stocks to bonds. Many people, especially retired, would prefer a safe 2% return over 7% return with occasional 50% crash (as in 2000 and 2008).

> stocks tend to fall when interest rates rise.

unexpectedly*

stocks tend to fall when interest rates rise unexpectedly.

many actual interest rate increases are followed by stocks rallying because a larger rate increase was expected & priced in.

> many actual interest rate increases are followed by stocks rallying because a larger rate increase was expected & priced in.

Right, but that just means more than 100% of the fall due to the rate increase occurred earlier when it was anticipated, so the rate increase still caused the fall, in effect.

The expectation caused the fall. It's possible to even have an expectation of a rate increase and then not have any at all.