My cat does this too. It started a while back when I had some photos sitting out on my desk in one of those picture holders where you just poke the photo in it and it's not in a frame. She chewed up 4 of my pictures and on one of them she chewed all the corners off of it. I had to stop putting photos in it. Then she started chewing the corner of a wooden picture from on my desk and clawing my door and tearing pieces of wood off it and chewing them. Now she's started chewing on the corner of the coffee table and other wood furniture. She also chews up our plants, but lately she has stopped doing that and has stuck to the wood.
It's really odd though because sometimes she'll be chewing on the corner of the coffee table and then start rubbing her head all over it. Crazy cat. lol She has Purina cat food that's the hard pieces as well as treats. So, I have no idea why she's been doing this.