Many old people are demanding, irritable and unbending. Has age anything to do with this?

Age of itself does not account for it. Such people were much the same when younger, admittedly to a lesser degree. There are certain types of personalities which, if not rectified early in life, will lead to the attributes you have mentioned in old age. Those who are cheerful, optimistic, positive, have a sense of humour and are concerned about others, will be unlikely to grow into grouchy individuals.