Take the phrase "vaccines cause autism" (using because everyone's heard it by now) there's research that suggests that in an attempt to debunk that you actually lead more people to believe that vaccines cause autism.

the reason is you're actually spreading the lie in an attempt to debunk it. So when you're debunking it you have to decide is it widespread enough that the risk of spreading the lie is balanced outby debunking it.

There will always be a group of people who are not available to be persuaded. The ultimate goal is quarantine not eradication. Plus it also depends on the tactics of the debunking.