Tell people they're right to convince them that they're wrong

No one likes being told they're wrong. So it's not surprising that when you do tell people that they're wrong, they often stop listening to what you have to say. On the other hand, if you start by acknowledging that their overall point of view is correct, but that you have suggestions, people are more receptive to changing their opinion. All of this is to say that people are better persuaded by arguments that they uncover for themselves than by arguments that they're told by others.

By changing the dynamic of the conversation from confrontational to collaborative, you're more likely to find compromise. And as a result, you're more likely to be given the opportunity to walk through the facts that people need to put together to convince themselves that they were wrong. It doesn't matter who gets the credit.