There are many reasons for irritability in the elderly. As before mentioned, alzheimer is a common one but many medical issues affect oxygen and blood flow to the brain and any of these may cause mood swings. Also, a number of medications can have a side effect of mood swings. It has been proven that if one stays physically and mentally active that it can actually help in slowing down mental impairments associated with the elderly. Hence, the card games, dominoes, dances, and quitting bees associated with aging are mentally beneficial. : )
Researcher have connected the Alzheimer's disease with fits of anger experienced by old people, and some even strongly connect this type of a reaction with the medications used to treat this condition. I also think anger management in the elderly is also strongly connected to an individual's personality and it could also be related to depression.
My father-in-law started displaying anger and it is linked to frontal lobe dementia. I also think many are just frustrated and scared because they can't move and think like they used to and are becoming less independent. This manifests as anger.