While wading through all these responses for the very specific response you are looking for (which some charitable LW'er will probably provide if this thread is commented upon frequently enough), you might want to read "How to Win Every Argument - An Introduction to Critical thinking" by Nicholas Capaldi. It offers a brief overview of logic and rational argumentation, and touches upon fallacies and what this site calls the 'Dark Arts', which should help in arming you against common attacks. If you are mathematically minded, but don't want to go into too much depth, you might want to check out "Sherlock's Logic".
Mind, the former text is more of a survey course, whereas the latter is more of an introductory course.

I have read that Luke Muehlhauser has worked through a dilemma similar to yours, and his blog you may find valuable.