What I was taught was try to take their conclusion and see how hard it is to maintain it. For example if someone were to argue with me about the truth of their particular branch of Christianity I should do is show how many assumptions I need to make to get to it. I.e. there is a god, this God is personal, this God favors human life, this God choose one particular tribe, this God waited all that time to send his son down.....
From a logical point of view, I tend to mostly agree. The issue is, however, that many people only really change their opinion when they figure something out by themselves. While, in an argument, they won't be able to come back with anything, they'll often still hold on to their original opinion. If your goal is to change somebody's opinion, it can often be more effective to drop subtle hints over time and make them come to their own conclusion.
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