What convinces is conviction. Believe in the argument you're advancing. If you don't you're as good as dead. The other person will sense that something isn't there, and no chain of reasoning, no matter how logical or elegant or brilliant, will win your case for you.
“I'm not trying to pull the rug out from under anybody, but the music really does tell you where to go.”
“Cruel and cold is the judgment of man, Cruel as winter, and cold as the snow; But by-and-by will the deed and the plan Be judged by the motive that lieth below.”