Although everyone wants to make a successful contact, find the right tutor or right student, sometimes it just doesn't work out. This happens to me occasionally, and my lesson has been--just move on, gracefully, politely, without hard feelings. Don't take it personally, it's a professional contact that sometimes misses.
For tutors, you should know your requirements, your limits, your preferences. You may prefer a certain age, a certain gender, a certain skill level for your subject. You should note those in your profile's introduction if possible, so that prospective students don't waste their time in contacting you if it's not right. You should also determine after the first, or at most, second lesson if you feel this student will work, and if not, politely inform him/her or the parents, of this so they can search for a better match. Of course sometimes the problem may develop slowly with time, and again you should let them know if it's not working in your opinion, and why not. Don't retain a student just for the money if it's not a good match--your evaluations and feedback may reflect this later.
For prospective students or parents, you should have a clear idea of why you choose to contact a particular tutor. Be very clear up front about your needs, goals, expectations. If you fail to explain your requirements at the outset, it's possible that the tutoring will fail, and it may not be all the tutor's fault. Decide if you want a younger or older tutor, a male or female, that best suits your or your child's needs. For example, I believe I am sometimes chosen as an older woman, but in fact, some students may better be helped by a firm male hand. And if it's not right for you, politely explain that you want to find another tutor, which is always possible. You don't even need to state your reasons, but don't stay with a tutor who isn't helping you, out of politeness.
Finally, there are sometimes personality differences between tutors and students. That happens--we are who we are--and again both parties should recognize it, and agree to end services politely. There are always other tutors, other students, and it's just business. Be prepared to move on without hard feelings.