Running

Many people have the impression that the human body is like a mechanical machine, it wears out with use and inevitably breaks down with age. But it is not.
The human body is a living, growing organism. It responds to the stress of exercise by growing stronger.
Yes, as we age, we lose a little resiliency, which means we have to be more careful of injury, because it takes longer to recover. But we never lose that ability to respond positively to the stimulus of vigorous physical activity.
I know people who have run into their 80s, and gotten really slow, but had no detrimental effects from it. On the contrary, they could still run 5 miles in a session. And they appeared to be much more healthy than their peers.
Medical studies have assigned senior citizens to weight training regimens to see if it could prevent falls, which often prompt a downward spiral towards death, and they got stronger. I don't remember off the top of my head exactly how old these people were. But I am assuming they were pretty old if the researchers were choosing them as people who had to worry because a physical accident could be the beginning of the end. AND they could still improve themselves with exercise!
I'm sorry. But your family is just plain wrong.