This holds for Catholics. Non-Catholic Christians are not bound by this canon.
We’re talking about someone prior to his entry into the Catholic Church. (For those in his family who are already baptized, this is a matter of “coming into full communion with the Church.” For those in his family who are not already baptized, this is baptism (and presumably First Communion and Confirmation), most likely at the Easter Vigil.)
One answer for the OP’s son is whether he himself believes in the teachings of the Catholic Church. If he does, then it doesn’t make sense to be baptized elsewhere. (If he doesn’t, then we have a potential problem: we’re not supposed to make someone Catholic against their will. It’s right in Canon Law. )
Another answer is along the lines of the comments given by @SuscipeMeDomine and @SMHW: baptism in the Catholic Church makes one a member of the Catholic Church and a member in this ‘family’ of believers. (Valid) baptism elsewhere only creates imperfect communion. Essentially, he’s asking, “why should I be in our family?”
Yet another answer might be that, while he technically could be baptized elsewhere, that would mean that he would not be able to receive Eucharist in the Catholic Church until he himself goes through the process his family is going through right now: the process by which they “come into full communion with the Church”. Does he really want to be baptized elsewhere, and then not fully participate each Sunday at Mass?
All things considered, his son’s question boils down to the question “aren’t these two (baptism at our old church and baptism in the Catholic Church) exactly the same thing?” The answer is no, they’re not exactly the same thing. There is a point at which the effects differ (namely, to what extent one can participate in the sacramental life of the Catholic Church).