Why is this happening?

Construction grade lumber seldom works out when routed. The soft parts between layers of harder material are perfectly designed for chip out like this. I agree that it's the material. For stuff like this, you need pretty flat, straight grained hardwood. Chair rails can get a lot of abuse over the years and soft pine will dent and look beat up pretty fast, particularly in a narrow dining room space or if there are kids around. Be careful in selecting hardwood at the big box store. Twists are awful to deal with, and you need to be very careful to select the straighted, flattest boards. Same wherever you buy your hardwoods. Out of any hundred pieces, you'll find maybe 15 or so that are OK to use. Pix is of common defects you can usually spot by looking down the piece you are considering buying. I rest on end on the concrete floor which gives me enough of a level base to make any defect obvious. Let the wood acclimatize a bit in your shop, usually a few days.

Oops, entered the pix twice New software asked for thumbnail or full pix, but I think it automatically entered the full pix first and when I then clicked full, it put the pix in again. OK, there's a lesson.

Also meant to add the following. While it's easy to find most major defects by eye, sometimes the problem is more subtle. You can detect these using two very straight sticks. Lay one across each end of the board. Sight down the board and notice whether there are any gaps and if the two sticks are parallel. This would be something you do after selecting the best boards you can find.

You also need to find a lumber yard that carries hardwoods near you. Check the web and any local woodworking or cabinet maker shops for where to get hardwood. These stores will also carry real Baltic Birch plywood. Once you use BB you will only use the big box ply for rough uses. The OK big box ply is as expensive as BB ply, but real BB is generally 5x5 ft., and has 2 to 3 times as many layers, all without voids so the edges are always solid. I think you can sometimes find larger, 4x8 sheets of ApplePly, American made, is available from certain sources.similar to imported Baltic-birch plywood, ApplePly is a premium plywood made from thin layers of birch and faced with various species of veneers. Made by States Industries in Oregon. I haven't found a local source yet, but my nearest lumber dealer is about 40 miles away.