See conflict as opportunity.
Sometimes conflicts provide good opportunities for helping your mentee develop problem-solving and conflict-resolution skills. You can start by asking your mentee what he thinks the problem is and how he feels about it. Validate his concerns and feelings; if you disagree at this stage, you will shut off further conversation. Even if what he says upsets you, do your best to stay calm and do not react emotionally (i.e., with anger or blaming). It is OK to tell your mentee how you feel in response while still acknowledging his perspective and conveying how committed you are to the relationship. Ask your mentee what he would like to change, and be open to his ideas. If you have made any mistakes, it is better to admit them. See if you and your mentee can find solutions to the problem you can both live with, and stress that this is something that you can get through together.