Don't deduct your pet, but ...
Yes, your dog or cat is a family member. And yes, some insurance companies now include coverage for Fido or Fluffy in auto policies.
But your affection for your pet or an insurer's willingness to pay for some of your domesticated animal's care doesn't carry any weight with the IRS. So don't you dare try claiming your pet as a dependent. Yes, it has been done. And yes, it is disallowed by the IRS when the furry facts are revealed.
You can, however, deduct as itemized medical expenses the costs of buying, training and maintaining a guide dog or other service animal to assist a visually impaired or hearing-impaired person, or a person with other physical disabilities.