Why do some passengers refuse to give up their plane seats for families, and is there a way to handle it that benefits everyone involved?

Some people pay for those seats for a reason. It helps to get them through the flight. They could be a nervous flyer and need the extra reassurance. Maybe they like the view. Maybe they took the time to work out where the best views would be from that particular side of the plane. Maybe it’s a position where the seat is less likely to be jolted so that they can catch a nap. Or maybe they need access to the aisle quickly if they need to use the toilet. If someone’s paid money to select that seat, they’ve done it for a reason and you have to respect that. The only way round it is to offer them compensation for moving. It could be an upgrade, a free drink, or a snack, gift or meal. It doesn’t necessarily have to come from the airline. It could be a gift as a thank you for agreeing to move.