Go, unfortunately, as I'm sure you know from experience, six years of age is not one where kids should be making such decisions. It's not Justin's fault he lost interest. I'd bet his parents don't listen to him at each opportunity they get, don't encourage him to keep going on a regular basis, and don't make him feel important because he's taking lessons. I got lessons after a few years of working with piano blues tapes that my dad had bought me. Eventually my parents figured I would do well in lessons since I was making a lot of progress with the tapes and using them consistently. I didn't take lessons from 8 onward because I was old enough to consciously choose to like lessons. I kept going because my parents and my grandparents supported me every day, went to all my recitals, and listened to me play at church. I played because my friends in school thought it was cool that I could play the piano. I played because it gave me a place in life, and it made me important to others. It wasn't until high school that I was mature enough to decide for myself that music was what I wanted to do. Children cannot make decisions for themselves, it is even proven in psychology (I took AP my senior year). Humans do not begin to mature mentally and differentiate until the teen years. That is why adults, as parents, MUST expose their children to music, dance, sports, all recreational activities, and encourage them and keep them at it until high school when the child is old enough to choose for him/herself. It's frightening to me how much a child's future depends on the parents' decisions in these early years, and I hope that when I am finally a parent I can do a good job for my children.
My only guess as to why my sister wanted to quit is that she wasn't making the progress I was, because she was two years younger, because she had a different life than I did, and because I can't imaging it's easy living under me (I was also salutatorian). She is making her own life with her voice, now. In reality, that was why she started wanting to quit. The true reason why she quit is because she did not like her teacher, and she got into a terrible fight with my dad over it and he refused to get her a new one. Mom, unfortunately, didn't make herself heard as much as she could have in this argument. She either remained with the teacher or quit, and she quit. But she is 16, now. Not 6. Of course, it's not your duty to parent for Justin, only to recognize that he did not make the decision to quit. He's just not living in the right environment for it.