It can be hard finding fabrics that your cat/dog wont scratch or chew up. I have a small Biewer Terrier (its a breed like a Yorkie) named polo who loves chewing. You might also have a dog or cat, and chances are they scratch or bite fabric and maybe they shed. So I can help you find a pet friendly option right now.
1. Synthetic fibers.
This isn't your only option but consider it they may not look the best but they work perfectly. Never use materials made out of tweed, it might be tempting but it is hard to clean. Polo (my dog) does not seem to scratch or bite on these fibers. I have heard that cats don't like it either.
It looks good aesthetically and is super cool. Dogs love it but wont bite or scratch it, same thing with cats. It is very easy to clean and even then it doesn't attract pet hair. I love it you love we all love it.
Let me just add some extra details:
Avoid the following fabrics for pets: silk, linen, chenille and tweed
Tweed is by far the worst. It is impossible to clean, do not buy tweed if you have a dog it is impossible to clean out the hairs. If you want to prevent stains on your couch then I recommend "ScotchGard" It is amazing because it prevents stains in your couch. It also prevents spills. So what are you waiting for? Get it now