Why do people get dry eyes when older?

Diseases/Medications. Adding to dr. May's answer - older folks also tend to have more conditions/diseases like thyroid disease, arthritis, etc and these can lead to ocular surface disease/dry eye. Medications, like blood pressure meds, diuretics, and antacids (like nexium) can cause dry eye. And the longer you live, the more you have been exposed to environmental effects of photochemical pollutants and pollen.
Less tear production. Elderly people frequently experience dryness of the eyes. With age the gland the produces tears becomes less efficient producing not only a lower amount of tears but also produces poor quality tears. Dry eye is more common after menopause this is related to hormonal changes.
Dry eye. Hormonal changes, natural age related decrease in tear film/lid glands, medications, dietary issues, systemic disease, etc.