You say that you have scratching posts around your house, but they may not be the right type. Cats have definite preferences for scratching surfaces, and something about that chair makes it "better" than the posts.
For example, we had a cat who LOVED to scratch on our ottoman. We had plenty of posts, but eventually figured out that we didn't have one tall enough for him - he wanted to get a good long body stretch, so the post had to be about 3 feet tall. Once we added a post of that height, he rarely touched the ottoman again (instead of a daily thing it became something he did once a month or two).
So, some things to consider:
- Material (cardboard, carpet, sisal rope, sisal material (rope and material have different textures).
- Size (a post should be tall enough for them to stretch their entire body, at least 3 feet; most pet store posts are NOT tall enough). Horizontal scratchers should be large enough to stand on while scratching (generally).
- Shape/configuration (post, horizontal, incline, specialty)
- Location (if your cat is scratching a specific chair, put the posts near the chair; another problem we had with the ottoman was that it was in the middle of the walkway, so it was super convenient, unlike the scratchers we had at the time).
- Lures (give your cat a reason to hang out with his scratcher; catnip, attached toys, attached lounge pillows, will all increase his feelings of possession to the scratcher and make him more likely to want to scratch (and put his scent on) HIS furniture).
In addition, make sure to keep their claws trimmed. Even if they aren't scratching on your furniture on purpose, running and playing across the furniture can cause damage. An alternative to trimming (which may help while you're figuring out what kind of scratcher he wants) would be to use nail caps. He'll still make scratching motions on the furniture (so you can monitor your progress with finding the right scratcher) but it won't cause damage.
You CAN have nice furniture even with cats! We have 4 cats and leather furniture. We occasionally get accidental scratches from running and playing, but nothing on purpose.
As a last note, declawing is NEVER recommended. Cats generally become more aggressive (especially biting) when you remove their claws because it's painful and you're taking away their defense mechanisms. In addition, as a declawed cat ages it will tend to develop arthritis on the paws which will make using a litter box painful, and cause an aversion to the litterbox. For more on the hazards of declawing, I recommend the Paw Project