Almost all the furniture that you buy these days have white plastic nail-in feet protectors. They also sell them in most hardware stores. Anyone thinking that these actually protect floors will soon find out that this is not the case. Many of them are just ½” in diameter.
Basic physics tells you that the smaller the surface the greater the forces exerted on that surface. You have a person sitting and moving back and forth on that little half inch circle, it’s bound to cause damage to the floor over time.
So, if you have those plastic nail-in feet protectors, take them off and put on proper floor protectors such as the Flexi-Felt floor protectors. Make sure to cover the entire bottom of the chair legs so that the weight of the person sitting in the chair is distributed over the entire surface and not on just a tiny ½” circle.