S.G.
It isn't unusual for kids to want to quit something they don't feel they are good at right away. They have no patience and are unable to understand that with practice you can do great things. When my kids wanted to do something we would let them with one rule... you have to finish out the season or year. This worked for everything from sports to scouts and as far as the piano lessons and swimming lessons, they had to do it for a couple years to learn to read the music and see if they have a talent for it. My oldest was one who couldn't get a song down and he was ready to quit over it. It was horrible with having to fight him to practice and such. He was about 8 or so. I suggested breaking it up and learning part of it then when he has that down to work on the next part. Soon, he had the song memorized and every place we went that had a piano, he would play that song. Once they were in band in school and had different instraments to learn and practice, I let them drop the piano lessons.
After you put money into a guitar I would insist he put in at least two years of lessons. Chances are he will pick it and want to stay with it.