Before his current birthday, when you divided by two you got a remainder of 1 which means that your father's age then was odd number. You get a remainder of 1 with any odd number by 2.
He's now had a birthday. The way to show this is 2n + 1 for his age before his birthday. He has a birthday so his age is 2n + 1 + 1 = 2n + 2 which is an even number and therefore not prime.
