As David Mamet says in On Directing, people don't talk to reveal themselves. They talk to get something that they want - approval, affection, money, sex, a reprieve from an impending death.
So figure out what the speaker wants from the person she is speaking to. Then figure out what her strategy - her sales pitch - would be, based on who she is, what she wants from the other person, and her own evaluation of what this other person is like.
You can look at this on different levels. Does the speaker really know what she wants? Is she fully consciously aware? People often decieve themselves about their real intentions.
When someone does explain themselves, it should set off alarm bells. Too much self-explanation can equal lying, self delusion, confusion etc. Somebody who announces, "I'm a really a simple guy," may be telling us that he's hopelessly complex.
And what about the speaker's evaluation of the person being spoken to? Is this evaluation accurate? If so, how did the speaker come to an in depth knowledge of this other person? If the evaluation isn't accurate, exactly how and why does the speaker misread/misunderstand the person they are trying to speak to?
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Another thing to consider is how effective the sales pitch is. Does the listener really hear what's being said, or does he interpret it through his own framework of wants and needs? In real life, people often don't listen to each other. People who've known each other a long time, like married couples, can have selective deafness.
They just don't hear, that is, they just don't acknowledge, what they find unacceptable. Like the devout Baptist mom who never seems to hear the "boy-" part of "boyfriend" when her out gay son talks about his vacation travel plans.
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Crickets! I am a chatty fvck today. Maybe it's the meth flavored soda pop.
Conversations aren't going to be very interesting if there's no conflict. But that doesn't mean that characters can or should speak directly about the conflict. There may be specific reasons why they can't speak to it directly, or they may just not be sure what's really at issue. Each person may have his or her own ideas about just what the conflict at hand is.
If the conflict is resolved too easily, in just the way that's required for the plot to march forward, the dialog might seem on the nose. It can be good to play with expectations, to have people behave in ways that aren't entirely rational. Sometimes people just refuse to go along, and conflicts that ought to be easily resolved, aren't.