In verses 9-10 of the Letter we read,
I wrote something to the church; but Diotrephes, who loves to be first among them, does not accept what we say. For this reason, if I come, I will call attention to his deeds which he does, unjustly accusing us with wicked words; and not satisfied with this, he himself does not receive the brethren, either, and he forbids those who desire to do so and puts them out of the church.Here we see John, having already written to this local congregation, was ignored and mocked by Diotrephes. To add to these sins, Diotrephes also refuses to receive certain brethren and expels those believers who don't agree with his policies. Some might be wondering: how does this refute Protestantism? My argument is that it refutes Protestantism by proving there is a hierarchy within the Church that cannot be simply overturned, even if those in authority are acting in an unjust manner.
Diotrephes only appears once in the New Testament, so these two verses are all we have to go by, but I believe they contain enough data to make my argument. Clearly, Diotrephes is in a position of ecclesial power, which includes the authority to excommunicate. But it is undeniable that John's authority is greater, indicating another level of hierarchy that even Diotrephes must submit to.
Reformed Protestant scholar Dr Daniel Wallace gives this summary: "The occasion for 3 John does not at all seem to be an issue of heresy, but one of pride. There is no real evidence that Diotrephes was a heretic." I would agree with this. The data suggests Diotrephes was prideful (i.e. "loves to be first") and insubordinate (to John), but that's distinct from heresy. (But even if Diotrephes was guilt of heresy, there is still no indication he lost his authority.) Thus, the situation here is one of schism, which is an impossible status in Protestantism since their is no central authority to 'break off' from.
Of course, Protestants must come up with an alternate explanation for this, since it refutes their very foundation, which is that of esselecial self-appointment and autonomy. The most important objection the Protestant must make is that Diotrephes was not a ecclesial minister, but rather a very influential layman, such as a wealthy politician. The problem with this is that the very functions Diotrephes was exercising were precisely that of an ecclesiastic. He is said to have loved being "first among them," meaning being prideful of his leadership position within the body, refusing entrance to outsiders, and excommunicating others. (No mention is made of him merely encouraging the true ministers of that congregation to do these things.) Further, there is no indication that Diotrephes had no such authority, else he could have been easily dealt with, such as John rebuking the true clergy or simply telling the local congregation to ignore this (lay) madman.
This Catholic argument can also be proven by showing the absurdity of the contrary position: if Protestantism were true, then Diotrephes's actions are perfectly justified. He would simply be his own, self-appointed Lone Ranger minister who could run his congregation as he pleased, and any outside interference would hold no weight. He would be in charge of his own self-made store. It would be absurd for John to write to this store in the first place and it would be absurd to worry about not receiving travelers. And, of course, it would be of no consequence if a believer was excommunicated from this store. Think about how Protestantism has always operated. Nobody tells another store what to do, and if someone is unhappy in one store they leave for another store.