Ted Neward: “... to truly understand something, you must see from a different perspective.”
This is one of my favorite aspects of law school - having to argue for a position that you disagree with.
Really, the best way to strengthen your argument is to make the counter-argument. This not only helps you understand the inherent flaws on your side, but it also helps you be more persuasive by understanding the light in which the other side will hear your argument.
This technique is especially effective when it comes to sensitive moral issues that are not so black-and-white - like abortion, same-sex marriage, racial profiling, and so on.