At the age of 12 a child can express where they want to stay - but that is in the context of a custody hearing that is either the first hearing, or based on a material change of circumstance. The child's desire to live with the other parent is not a material change in circumstance. The moves are also not a material change in circumstance. And, a lot of states are now enacting laws that prohibit using a military members deployment or duty station assignments in a custody decision.
Is there a reason that the child wants to leave? Has something happened? How are the child's grades and behavior? It sounds to me like he might be feeling that he needs to show some loyalty or alignment with you guys, and this is how he's trying to do it. It's hard for kids to be split between parents, and if he feels that you guys are really upset about it, or that you guys really want him to come live there, he may feel the need to make you feel better by saying these things. It's very common.
BTW, it irks me to hear people use the sacrifices military members make for our country against them when it comes to their children. We don't want to get moved around constantly and be seperated from our family either. But we do it, because that's part of the job.