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Number two is, how do you get an argument to be clear and straight to the point so that the person on the receiving end doesn't just try to shut it down but instead consider things from your point of view?
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This depends heavily on your listener. The first thing to do is listen to what they're saying. This will give you a good idea of what their perspective is, and (if applicable) what kind of fallacies they're operating under. Then you can direct your message to their assumption, rather than talking about a different area that will be viewed in a skewed manner because of their different (perhaps flawed) perspective, or viewed as beside the point.
For example, let's say you're asked to describe how a telephone sends someone's voice across the country. You might be describing how satellites relay the signal, when the other person is really wondering how sound moving through the air turns into an electric signal. By asking a few questions about what the person means or understands, you can save a lot of unnecessary difficulty.
Also, this asking and listening tends to affect someone's mood. People are more receptive to your ideas when they feel that you're listening to and understanding them. Your tone of voice influences this as well; getting frustrated and angry changes the tone of your voice, which in turn tends to make the other person less receptive and more difficult. In your money example, the other person calling you careless impeded the discussion by surprising/shocking/offending you. It was, perhaps, a poor choice of words. It also indicates a difference in perspective that should have prompted you to investigate their point of view. I suspect that while your point of view was "leaving money lying around is convenient, at the minor cost of not stealing" their pov was "the minor cost of putting your money in a more secure place protects you from loss and theft". From this understanding of different perspectives you can move to a more productive discussion about the relative merits of each side, provided everyone can keep their emotions in check.