If you are at all adept at listening, you're likely to hear things about your students' learning strategies, such as whether they learn better by reading or doing, and whether they respond better to coddling or criticism. These are things it would ordinarily take weeks or months to learn by trial and error in the air, by which time one of you may have quit.
As far the students are concerned, they're simply telling you a story about their past. What they are in fact telling you is a lot about their future with you. There is a lot to be learned by asking the right question, and then listening carefully to the answer.
Remember, during the first few lessons your students are usually on their best behavior, often trying to fit their style of learning to your style of teaching. It's not until they feel comfortable with you that they allow you to see their real selves. This is when efficient teaching begins, and the sooner you get there the better for everyone. So help your students learn by getting them to quickly reveal the qualities they find useful and meaningful in a good instructor. Start by asking them a good question. That's the answer.