Yes, we do tend to get difficult in old age, and sometimes It's just age and nothing more... but sometimes it's a sign of dementia or Alzheimer's. If you think your dad may be developing that kind of trouble, please ask a doctor to evaluate him for it. There are medicines now that can slow the advance of these illnesses, and the sooner the diagnosis, the better.
My father has Alzheimer's, and what you described is the kind of exchange that happens several times a day in our house. But he's still himself at times, too, so that's good.
The other day he scared me to death, though, referring to something that happened in 1999 as "two years ago." When I pointed it out to him, though, he took a moment and realized what year it really is. Thank heaven.
I hope your father isn't sick -- I hope he's just an ordinary Grumpy Old Man!