Why are eyes so vulnerable to damage?

Ultraviolet Light. Uv light cause damages to cells. The melanin containing cells in the skin provide some protection for the body but the cornea of the eye is clear and allows the uv light to penetrate. This can cause damage to the lens of the eye resulting in cataracts.
Not really. Eyes are well protected with a bony outer frame, quick reflexes such as rapid eye closure, sensitivity, and a very rapid and efficient outer healing. If something gets through all of that, and gets to the interior of the eye, then really bad things can happen but most injuries of the face spare the eyeball itself.