Why is some of the skin on my neck very stretchy?

Variability. Everyone varies in their skin elasticity from person to person and body location to location. This changes with skin thickness, as well as age and history of sun damage or exposure to other agents/substances.
Loose skin. It is natural for skin to appear loose as we age. This is caused by a loss of collagen in the skin, which provides elasticity and allows the skin to stay in place. Other factors that contribute to loose skin from aging include the effects of gravity over time and the loss of muscle or fat tissue under the skin. An example of loose skin caused by gravity are sagging, loose eyelids.