How come I have cervical spondylosis, but nobody else in the family has it?

Very Common. Spondylosis is basically a fancy term for wear and tear of the spine. We will all develop wear and tear over time and generally don't know it. Spondylosis is seen on xrays or MRI as degeneration of the discs or joints of the spine. It is often not painful but certainly can be. It is more common to see spondylosis as we age.
Incorrect. Everyone else likely does have it. They just don't have symptoms. Degeneration is ubiquitous. Like wrinkles of skin, ddd happens. Doesn't mean you're disabled or will be. Be proactive. Core exercises, nsaids as needed, ice/heat, salonpas hot patches. If not improving, seek medical care. Mckenzie pt works great, but needs doctors rx.