One of the biggest differences I have experienced between analytics and product management is the difference between understanding a decision and being responsible for making it.
In analytics, I was often trying to understand what happened, why it happened, and what the data suggested we should do next. That trained me to ask good questions, look at a problem from multiple angles, and be comfortable with evidence. Those are useful skills in product as well, but they are not enough on their own.
As a PM, there is a point where the analysis has to stop and a decision has to be made. You rarely have all the information you want. There are competing priorities, imperfect data, different stakeholder perspectives, and consequences that may only become visible later.
That has made me appreciate product judgment more. I still think data is extremely important, but I increasingly see it as a way to improve judgment rather than a substitute for it.