I have learned that only two things are necessary to keep one's wife happy. First, let her think she's having her own way. And second, let her have it.
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.
There are plenty of recommendations on how to get out of trouble cheaply and fast. Most of them come down to this; Deny your responsibility.