According to Roman Catholic interpreters, the verses noted above mean that the Holy Spirit will lead the apostles and their successors into much more truth than Jesus has yet given them. That undisclosed truth they could not bear, or could not profitably receive. The sort of truth intended here, they say, includes doctrines not yet fully developed, like those concerning Mary -- doctrines that articulate her perpetual virginity, her immaculate conception, and her bodily ascension into Heaven. They also include doctrines more fully articulated later by the church in its ecumenical councils, like the doctrine of the Trinity and those centered on the incarnation.
Additionally, according to the Roman Catholics with whom I have debated, (and for the rest of this paragraph I employ their own words) apostolic succession is clearly indicated in these verses because (a) the doctrines noted above were not fully articulated during the apostles' lives, and, more importantly, because (b) those doctrines had not been challenged, and therefore did not need to be defended by the apostles, which is what "you cannot bear it now" (v. 12) means. Therefore, being led by the Spirit into "all truth" is a promise and a privilege intended by Jesus not simply for his apostles, but also for their successors when those truths are revealed later. Most of the information to be imparted in the future would not have been relevant to the apostles, whose theology was unassailable while they were alive. In their absence, the Holy Spirit will lead their successors into "all truth" (v. 13). This passage, therefore, is a guarantor both of apostolic succession and of the RCC's supernaturally endued reliability in matters of faith and morals because the Holy Spirit Himself is utterly reliable.
On the contrary, it seems to me that in this passage Jesus intends nothing of the sort asserted by my Catholic colleagues in their interpretation, as a careful examination of the passage in which these verses occur will demonstrate.
In verse 1, Jesus tells his disciples that the rather chilling things He has told them so far (15:18ff) were told them so that they might not stumble when the difficulties He mentioned actually begin. He is forewarning them so that they might be better prepared for their coming troubles. Those coming troubles include persecution by their fellow Jewish countrymen, who will think that by harassing the Christians they are doing God's work (v. 2; Cf. Acts 8: 1ff.). By forewarning his followers, Jesus is giving them information they could look back upon later with profit (v.4).
His own task, He tells them, is to return to the One who had sent Him, a fact that left them deeply sorrowful (vv. 5, 6). In order to assuage that sorrow, Jesus explains to them that his departure, far from being a deprivation, is indeed a great benefit because it makes possible the coming of the Comforter (v. 7), whose own task is twofold -- one task in reference to the world at large, and one task in reference to the apostles themselves. Regarding the world, the Comforter will reprove (that is, convict, convince, or persuade) it about sin, righteousness, and judgment (vv. 8-11). Regarding the apostles, Jesus has many more things to tell them, but because of their weaknesses and burdens, He delays his telling (v. 12), which will be carried out in His absence by the Holy Spirit (v. 13), Who will lead them into all the truth that Jesus wants to tell them now but that they could not bear at the moment, truth pertaining to their coming troubles, as the context makes clear. They are to face great sorrow, the details of which are not yet given to them, except this: While the world cheers the apostles will weep and wail, much like a woman in labor (vv. 20, 21). But when it is over, they are destined for great and enduring joy (v. 22).
Nothing at all in this passage is either spoken or implied by Jesus about apostolic succession or about Roman Catholic infallibility in matters of faith and morals. Only the most egregious and self-serving eisegesis insists otherwise.
Jesus is not assuring His apostles (1) that all that they and their unmentioned successors will believe in the future pertaining to faith and morals is going to be true, or (2) that all the things they and their unmentioned successors believe in the future will be the result of the Spirit's leading, or (3) that all they and their unmentioned successors believe in the future will glorify Christ, something that characterizes things truly revealed by the Spirit (v. 14). Instead, when the apostles comprehend some currently unbearable truth about their coming travail -- truth that glorifies Christ -- it will be because the Holy Spirit has led them to it. All such truth comes from the Spirit, and, hence, from Christ Himself. The "all" (v. 13) that describes the truth they are yet to receive is not universally inclusive, but is truth of a specific sort, truth pertaining to their coming troubles, truth that glorifies Christ after He has departed. Jesus is not promising them and their unmentioned successors that they will learn literally "all" truth about faith and morals, much less that they will learn literally "all" truth whatever. He says no such thing. They are not here promised the truth about exactly how many grains of sand lie on all the beaches in the Caribbean, or about how to clone dinosaurs for breakfast food, or how to master cold fusion. Nor is He saying that all they and their unmentioned successors teach in the future on faith and morals will be true. He has in mind truth of a particular sort and for a particular purpose, to which He has been alluding continuously all the way back into the previous chapter, truth about the apostles' coming ordeals, truth that they were in no condition to receive at that moment.
The text does not say, for example, that all that Peter or his alleged successors teach on matters of faith and morals will be true and will be given to him or to them by the Spirit. Such things are simply not in view in this passage. Nor does it say that Peter and the apostles will even have successors, much less anything about the reliability of their future teachings.
If John 16:13 meant that after the Spirit was given to the apostles they would teach all truth and only truth, then Jesus would be flatly mistaken because after receiving the Spirit Peter, for example, sometimes lived and taught in ways that denied the very gospel itself -- clearly a serious fall from "all truth" on the chief apostle's part. Sometimes Peter did not believe, teach, or act according to the truth, much less all of it, and was not being led by the Spirit into unbearable truths when he did so. Following him can -- and did -- lead Christians away from the truth and away from the gospel.
Nor do these verses designate the RCC as the infallible arbiter of future theological disputes, such as occurred later in the various ecumenical councils. That reading of the text is baseless, tendentious, and anachronistic.
God Himself, not the RCC, will resolve all discrepancies -- theological and otherwise -- though it seems as if He has left their full and final resolution until the end of time. Short of that, the issues that sometimes vex us probably will not be resolved. I do not identify God's resolution of those discrepancies with the decisions made about them by the RCC. Nor does this passage in John.
To make my point from a different direction: The truth that comes from the Holy Spirit is truth that glorifies Christ (v. 14), not truth that glorifies one group of those that follow Him over all others. Therefore, I doubt that the self-glorifying claims of the RCC on this point are the truths that Jesus has here in view.
Nevertheless, Roman Catholics with whom I have discussed this passage assert that apostolic succession and infallibility are, to quote them, "clearly indicated." But I deny that something is "clearly indicated" that is neither mentioned nor even hinted at, especially if that something is allegedly three or four centuries in the future, as are the ecumenical councils to which my Catholic friends say Jesus is alluding. If such infallibility truly were "clearly indicated" here, that clear indication would be something more specific, like the mention of Bethlehem as the birthplace of the messiah in Micah (5: 2) centuries before the fact, or like a virgin conceiving a child, as is perhaps predicted in Isaiah (7: 14). But even that unclear and debatable prediction in Isaiah is exceedingly more "clearly indicated" than the things that Catholics claim to find in these verses. Indeed, if ecumenical councils and their decisions are present here in John 16, along with apostolic succession and doctrinal and moral infallibility, that fact is not clear at all. Furthermore, I strongly deny the Catholic assertion that the notion of "unbearableness" in verse 12 means anything like "irrelevant to the apostles," as if Jesus were cryptically referring to Marian and Trinitarian issues that had not yet emerged.