These are pics of my 33 foot fence that I have renovated. I am using the old posts which are 4 inch which are approximately 15 years old. I am taking off the old panels which had vertical boards and have applied horizontal boards.
I think for your son and his neighbor that 4 inch posts would have been sufficient but if the neighbor wants 6 inch then they can decide. All my posts were pretreated with a bag of cement at the bottom of each post for stability. Fence boards are pretreated. I took a chance of using the original posts. I cannot imagine taking out the old posts with 50 lbs of concrete attached at the bottom. 5 feet above ground and three feet below. It has been a manageable project by myself. 4 inch posts were a lot easier to handle by myself than 6 inch 15 years ago.
Cheers, Guy.