I wrote - The oldest manuscripts add “something”: a communication, probably, on the subject of receiving the brethren with brotherly love (3Jo 1:8, 3Jo 1:10). That Epistle was not designed by the Spirit for the universal Church, or else it would have been preserved.
unto the church - of which Gaius is a member.
loveth ... pre-eminence - through ambition. Evidently occupying a high place in the Church where Gaius was (3Jo 1:10).
among them - over the members of the Church.
receiveth us not - virtually, namely, by not receiving with love the brethren whom we recommended to be received (3Jo 1:8, 3Jo 1:10; compare Mat 10:40).