They always have their own separate ways, of course. But sometimes they also move in the same direction. And sometimes they don't. The correlation as well as the decoupling that you are talking about are both temporary. Which could mean that despite an occasion or two where there is recorded peaking and bottoming of both Bitcoin and S&P 500 at almost the same time, everything might just simply be spurious correlation.
At the beginning bitcoin seemed to be an asset that had a negative correlation to the stock market and most people interpreted this as a sign that bitcoin will do well under the scenario of an economic crisis, however as institutional money has come to the market we are seeing that instead of a negative correlation we are seeing a positive correlation and it makes complete sense if you think about it.
If the same people are invested in the stock and the bitcoin markets then if the stock market goes down then the people that are invested in both markets and got profits out of bitcoin will sell their positions in order to cover some of the losses they had making the price of bitcoin to go down with some slight delay compared to the stock market, this does not mean there is something wrong with bitcoin it just means some people are trying to recover some of the money they lost and bitcoin is just on the middle of all of this.
