Do Rising Interest Rates Really Hurt Stocks?

Lots of chatter about rising interest rates and how that will affect stocks. I see no reason to guess. Let's look at the data.
The chart shows inflation (orange) US interest rates (blue) and the S&P 500. Correlation between the S&P 500 and interest rates is shown at the bottom.

I notice a few things:

--Stocks tend to rise slightly more often than they decline while interest rates increase. If you look at the periods where interest rates rose, more often not stocks did too. But this is pretty much a coin flip.

--Sometimes interest rates move with stocks, sometimes against (correlation at bottom).

--Sometimes stocks fall after the rate increases stop, other times stocks rise. Again a coin flip.

This leads to the final conclusion:

--Interest rates are a poor indicator for stocks. Trust the price action of the stock index, and don't get bogged down thinking about interest rates as a relevant variable.

What am I missing?

Comment:

Even massive jumps in inflation (like now) are mixed. In 1973 stocks went down (it had been choppy for a 8 years already, so price was basically staying in its range.

In 1977-1979 stocks dropped about 10% initially and then rallied after that.

Comment:

Out of 10 periods of interest rate increases since the 1970s, stocks rose during 7.5 of them (0.5 because during 77-79 stocks dropped for a year and then rallied for a year while interest rates rose).

So if anything, rising rates actually tend to be more associated with stock price increases than declines.