**Core Concept**
The question is testing the knowledge of joint involvement in various types of arthritis. The underlying principle is the unique characteristics of each arthritis type, including their typical affected joints.

**Why the Correct Answer is Right**
Ankylosing spondylitis (AS) primarily affects the spine and large joints, such as hips and knees. However, the involvement of the joints of the hand is relatively uncommon in AS. This is because AS is an axial spondyloarthritis that predominantly affects the axial skeleton. The disease process in AS involves inflammation of the spine and sacroiliac joints, leading to fusion of these joints in advanced cases. The hand joints are not typically involved in the disease process.

**Why Each Wrong Option is Incorrect**
**Option A:** Rheumatoid arthritis (RA) is a common cause of hand joint involvement. RA is a seronegative spondyloarthropathy that affects the small joints of the hands and feet, leading to symmetric polyarthritis.

**Option B:** Psoriatic arthritis (PsA) can also involve the hand joints. PsA is a type of spondyloarthritis that occurs in patients with psoriasis, and it can cause inflammation of the joints, including those in the hands.

**Option D:** Osteoarthritis (OA) is a degenerative joint disease that can affect any joint, including those in the hands. However, OA is not as likely to cause symmetric polyarthritis in the hands as RA or PsA.

**Clinical Pearl / High-Yield Fact**
Remember the "SAFER" mnemonic to help you differentiate between various types of arthritis: Spondyloarthritis (AS, PsA), Axial (AS), Fibromyalgia, Enteropathic (e.g., Crohn's disease), and Reactive (e.g., reactive arthritis).

**Correct Answer:** C. Ankylosing spondylitis.