The story below is one I was told when studying for my Masters in Public Health. It is always what I come back to when I want to remember or explain the fundamentals of why prevention is important.
A man was fishing in the river when he noticed someone was drowning. He pulled them out and attempted to resuscitate them. Shortly afterwards, he noticed another person in the river and saved them too. He then noticed another, and another and another. Soon he was exhausted and realised he would not be able save all of the drowning people.
He went further upstream to find out why all these people were falling into the river.
On arriving further upstream, he discovered a broken bridge was causing people to fall into the river and end up drowning where he had been fishing. He decided he would fix the bridge to stop them falling in, instead of fishing them out after they were already drowning.
The aim of public health is simply to work upstream – fix the bridge and stop people drowning in the first place. Doctors are fishing people out who have started to drown. When put this way, I think preventing illness before it occurs seems vital.