In some cases getting someone to think in a way similar to yours or changing your mind is especially important. Besides the usual value for your correct reasoning, there’s an immediate decision at hand which is directly dependent on the result of a conversation or argument.
Being non confrontational is really useful in these situations, but requires particular sharpness and preparedness. You need to understand the issue as well as possible, and a quality I can’t quite defined but have observed recently… it’s a mixture of believing in the best cognitive intentions of your counterpart, as well as trusting their smarts and being genuinely curious. There may be other factors that further help you get into the right frame of mind.
The behavior I’ve observed in people who work like this – I’m not particularly good at this approach, although I’ve somehow pulled it off on some rare occasions – is an apparently open but directed curiosity which drives everyone into the meat of the business and enlightens everyone… and is equally likely to change anyone’s mind, except that the driver, the one projecting conciliation, has a deep understanding of the issue at hand that makes them especially likely to be closer to a good answer to the problem at hand.
This kind of attitude, which is also very calm in the conversation, is the best I’ve seen to steer important meetings in the right direction – whatever it might be. It costs a lot of effort, but practice makes master… perhaps doing it in non-crucial subjects is a good idea from time to time.