To tell someone they're wrong, first tell them how they're right
Learning how to do this is an essential skill. Most people are not idiots. If they disagree with you, it's probably not because they are being irrational, but because they're starting from a different premise, making different assumptions, or assigning different values to different aspects of the problem. Only when you understand their argument well enough to articulate it in your own words can you effectively present a counter-argument that has a chance of being persuasive.