How to Contradict People

Here's a situation I often find myself in: I'm talking to someone and they say something I disagree with. Should I loudly interrupt and give them the reasons they're wrong? Common decency would suggest not. Should I just ignore the incorrectness? Sometimes, but my dedication to accuracy moves me to say something more often than not. Here's my solution:

After the person has finished their thought, nod and say, "I agree with what you're saying." Follow up with a sentence that brings up the idea that there is conflict about this idea. Next, present your arguments, using a tone of voice that sounds like you're still defending their point of view. 

By the time they've realized you've contradicted them at every point, the subject of conversation will probably have changed. If they're sharp and say, "you just disagreed with everything I said," laugh and say, "wow, I suppose I did. [Subject of disagreement] is interesting like that."

Here's a short example, a reply to a classmate who suggested on the class discussion board that it would be better for humans to be closer to nature, i.e. use fewer or no artificial products:

"I also like thinking about natural resources like plants that we could use more diversely and effectively. Interestingly, there are some plants (like Guaiacum officinale L.) that have become endangered because of overuse as medicine. It seems that humans living close to nature are liable to take what they can and give very little back."