Somebody must have not been treating that chair right. A chair will hold an awful lot of weight sitting on top of it with the legs going straight to the floor. But when you kick them or knock them over or just hit them with things; chairs are not designed for that. The legs will break. You cannot just put a little peg on the leg to repair it. The leg was designed to a certain size and if you put a little peg that is smaller down in size, it's not going to work. I learned from an old German cabinetmaker years and years ago to put a piece of steel inside the leg and you'll never see that leg break again. You may break that leg, but you will never break it at that point again because the steel doesn't break.
