It is interesting to me that the scriptural warrant for confirming those baptized speaks not only of confirming them, but also of confirming the church: Elders are "to confirm the church by the laying on of the hands, and the giving of the Holy Ghost" (D&C 20:43). Not only is the individual strengthened by the laying on of hands for the Gift of the Holy Ghost. So is the Church.
I am stronger when I am with others who have been strengthened, when I am with others who have the witness of the Holy Ghost and who bear witness through the Holy Ghost. When we have the Spirit, we are stronger together than we are alone. Confirming one confirms all.