When first meeting a new person, in any social context, it can be a daunting prospect. When you include that there is meant to be a teacher/student dynamic and this dynamic can become even more daunting. It is important for tutors to build rapport with a tutee to establish trust, comfort on the student’s part that their tutor knows the subject and comfort from the tutor’s perspective to know the tutee will learn.
To help build rapport, we would suggest you begin by not talking about the subject at all. Students open up more naturally when you take an interest in what they do outside of the lesson environment: their hobbies, a TV show they’re currently watching or their main motivations are all key ways to get to know and build rapport. A light bit of humour, appropriately applied, will also allow your tutee to see you as a human first, tutor second. This can then lead to a fruitful tutoring relationship, all started from the initial procedure of taking an interest in the person behind the student.
Once this rapport foundation is laid, you can then move forward to show them that you are a person to be trusted in guiding them through their education and/or skill building. The aim is not to be their friend, but to reach a plateau where they feel comfortable to learn and you to tutor.
Give it a chance and let us know how it works for you.