Cats scratch to mark their territory - which is why they love couches so much!
Every cat scratches things. It's not just exercise and a way to loosen the shed claw covers, it's primarily a way for your cat to mark her territory. Many carnivores mark their territory by scratching - including bears and tigers, who scratch tree trunks. The higher the scratches are located on the tree, the deeper the scratches, and the more prolific the scratching, the more trouble you know you're in!
Your cat works on the same principle, just smaller. And on the arms of your couch.
It's obvious to see why a cat would want to mark the couch. First of all, couch arms are very scratch-able. You can really dig your claws into that nice plush fabric! Second, the couch arms are vertical, which makes a nice signpost. And third, your cat is probably pretty fond of your couch, and wants to mark it as her own.
If you want to save your furniture and your sanity, you need to get some proper scratching posts. And if you want them to be used, you have to put them in the right place!
My all-time favorite scratching post was built for me by my uncle. It's a sheet of construction-grade plywood with a deck post attached. Every few years I reupholster it with remnants from the fabric store. It's sturdy, tall, and won't tip over when my cats scratch it. These are all the qualities a cat looks for in a scratching post.
Every cat prefers a different texture. You may have to try a number of different surfaces before you find one your cat likes. Few cats like the carpet that usually covers scratching posts. Look for posts with sisal, burlap, rope, and the new kind made of vertical layers of corrugated cardboard. Let your cat sample them in order to choose what she likes best.
Don't just cram it in the corner of the room. Put the post somewhere prominent, like the edge of an entryway, or a corner that is the focus of the room. If your cat already scratches the couch, put a scratching post right next to it. Every time your cat reaches for the couch, redirect her to the scratching post. (Put some catnip on it, to make it extra-enticing.)
You may think "A scratching post is kind of an ugly thing to be staring at all the time." But you know what's really ugly? A couch that's been scratched half to death! I think you will agree, a scratching post is a work of art by comparison!