What is this?
Reversing is simply the unnatural act of "answering" a question with a question of your own.
Why is this important?
Reversing allows you to dig deeper into the issue that prompted the original question. In psychiatry there is a long-held, basic tenet that the problem the patient presents to the doctor is not the real problem. Psychiatrists use questions to probe into the problem at deeper levels to get a better understanding of both the problem the patient has as well as the potential motivation the patient has to deal with it.
In persuading others to do something beneficial to their self, it is helpful to not assume you understand their problem or their motivation nor to proceed too quickly into prescribing mode unless there is some kind of emergency. Most persuasion does not occur under emergency conditions, so it is more appropriate to dig through a few layers of emotional protection to find the real issues and the level of motivation the person has to invest time, effort and money to fix them.
Often people over-estimate the level of motivation someone possesses to fix a problem and over-emphasize the acceptance of their "prescription" to fix it. This tends to generate resistance and can easily get a persuader into a frustrating battle of "wills" with the person they wish to persuade. Through the use of reversing, a persuader can more easily keep the focus on - and get to the root issue. While focusing on the root issue it is easier to positively impact the motivation to do something about it.
Negative-reversing is a variation championed by David Sandler whereby the reversing question is posed negatively. For example: "Mr. Persuader, I have a problem I would like to fix" - "You really wouldn't want to do anything about that problem now though, right?" This style of reversing capitalizes on a person's somewhat natural desire to "disagree" with the person in the process of persuading them.
Just like reverse-psychology, negative-reversing is not always appropriate. Reversing in general is appropriate in most persuasion cases and although slightly time-consuming, ultimately shortens the persuasion process and improves the results.