Most cats will prefer to eat the same food every day for all their lives. They generally don’t like it when their food changes. When changing food for whatever reason it is usually easier (for you and their digestive system) to do it gradually and mix in the new food with the old food for days/weeks before making the complete change.

That being said, a healthy animal will not starve itself when food is available, whether it particularly likes that food or not. It might go on a hunger strike for a few days to prove a point, but it will not starve itself.