Being able to make the other person's case and articulate it in a way that is true to them is a key step in negotiations books, as well as some conversations books. It's not really hard to understand why. A lot of time is lost in arguments/debates because one person thinks the other person isn't understanding (even when the other person does) - so it's important to signal that you understand.
There is a kind of corollary to this: Often times person A comes to me complaining about person B being stubborn about something. So I often ask: "So why do you think B is insisting on it?" They usually cannot come up with a good answer. At that point, I either hint or explicitly tell A that B has a position that A doesn't understand, and it's not surprising B will not change his position since A isn't trying to address B's needs.
I first saw this principle as a negotiation tactic in "Never Split the Difference", he talks about how FBI hostage negotiators talk to understand the motivations of hostage-takers and terrorists without necessarily giving in or agreeing with any of those motivations.
It turns out even hardened criminals want to be heard/understood, and by using (author calls) "tactical empathy", you can start your negotiation off on the right footing.
There is a kind of corollary to this: Often times person A comes to me complaining about person B being stubborn about something. So I often ask: "So why do you think B is insisting on it?" They usually cannot come up with a good answer. At that point, I either hint or explicitly tell A that B has a position that A doesn't understand, and it's not surprising B will not change his position since A isn't trying to address B's needs.