Throughout the history of Buddhism there have been controversies about the ideas of irreversibility and of determinism.These are to do with the inevitability (or not) of future arrival at nirvana, either for individuals or for all beings.
Thus, in the Mahayana, in many scriptures, Buddhas give predictions of enlightenment to individuals or to whole groups. These are thereby singled out for their faith, having reached a degree such as will inevitably put them on an upward learning curve from which there is no return. In the Pali canon too there is the well-established typology of four grades, namely, arhat, non-returner, once returner, and stream entrant. These are all categories of persons for whom enlightenment is either already attained or inevitably assured. In Pureland, there is the idea that those who have faith are assured of entry into Sukhavati and that the conditions in Sukhavati are such that enlightenment is ultimately assured. Thus, in a sense, those who enter Sukhavati are "non-returners" unless they have made bodhisattva vows in which case they abjure entry into nirvana until all sentient beings can do likewise.
The fact that some are irreversible implies that others are not. Thus there is no inevitability about all beings reaching nirvana ever. At the same time, many Buddhists in history have believed that it was inevitable that all would get there eventually. Sometimes, of course, it is rather difficult to tell where hope stops and belief starts since both deal with matters that cannot be known for sure.
Now, in Buddhism belief is less vitally important than it is in some other religions. It is more the sentiment of faith that matters rather than the precise definitions of belief in this or that doctrine. Since one of the primary beliefs is that we are all deluded, one can hardly expect the ordinary practitioner to understand everything perfectly. These various ideas can be seen as the way that different groups of practitioners or different teachers have given expression to their faith in different times and circumstances. So I will attempt here to give my own take on the matter, but this does not mean that what follows is holy writ. Each person finds his or her way.
Faith as Condition
I take it that there is no determinism, but that things proceed in dependence upon conditions. Certain conditions, while not deterministically causative, are strongly conducive. If a person is in desperate thirst in the desert and sees an oasis in the distance it is highly likely that that person will head in that direction. He or she could go the other way and soon perish, but the conditions are strongly conducive. Buddhism has such a structure. When we experience samsara as being like desperate thirst and nirvana as a cool oasis, we are very likely to go there. Or, to put the same thing in more Pureland terms, when we really face our bombu nature and also get a strong feel for the grace of Amitabha we are very likely to turn our steps in the Buddha's direction and entrust ourselves to him. I think from this analogy one can readily understand the relationship between faith and clear seeing. Some schools emphasise one aspect, some the other, but it is all the same thing. Faith is the crucial condition and it goes with clear seeing of the spiritual-existential plight of being in samsara.
As best we can tell from the records, there was a controversy early in Buddhist history around the question of "falling back". Some people who had come to be designated as arhats by the Buddhist community were later found to have not been quite as holy as had been assumed. This led to the question whether (a) their designation as arhats had been a mistake, or (b) they had been arhats once but later ceased to be so, i.e. they had fallen back. According to the four grades theory falling back was supposed to be impossible. However if that led to (a) being the correct conclusion, how was the community ever to have confidence in its teachers? A difficult dilemma indeed.
A parallel problem has occurred in contemporary Buddhism since there have been a number of instances where teachers have designated "Dharma heirs" who then turned out to be corrupt in one way or another, exploiting disciples sexually, embezzling money, or just generally living in a self-indulgent manner. Does this imply that they fell back, perhaps corrupted by the privileges that came with the acclaim accompanying their status, or does it mean that the previous teacher who attributed that status got it wrong? If the latter, what does that imply about that teacher's supposed wisdom and judgement? These have been difficult dilemmas in a number of contemporary sanghas.
There is, here, a danger on both sides. On the one side there is the danger of the guru-personality cult. On the other side there is the danger of cynical rejection of the process of transmission. Buddhism is a transmission. It is not simply a matter of people working it out for themselves or passing an exam. One can know everything intellectually and still be less enlightened than a person of simple faith and such faith needs the confirmation that comes from the mirror relationship with at least one other such person. The trouble is, however, that this transmission process is not something that can be technicalised. It cannot be made into a social convention. Having the right papers and so on will never substitute for genuine sanctity. We can say that the core of it all goes on unconsciously. This means that one can never know for sure. You cannot know for sure that the person sitting next to you on a bus is or is not Quan Shi Yin Bodhisattva.
As usual, the solution to all these dilemmas lies in the middle ground. swinging to one extreme or the other is delusion. Buddhas can give predictions of ultimate enlightenment when they see such faith in a person that that person is on an upward spiritual climb, but even then the person will have ups and downs - in fact, they are likely to have even more extreme tests since they will pursue their path less inhibitedly. It is certainly not a matter of election by a community of deluded beings. Yet, at the same time, communities of deluded beings do naturally gather around persons that they believe to be spiritually advanced and this is not a bad thing, even though it might, from time to time, prove to be mistaken. Fortunately it is the case that having faith in a false guru can sometimes still be productive, since the purity of heart of the disciple is itself a powerful condition. Ultimately each is on their own path - ekagata - yet that path is a succession of encounters with others and in every encounter there is something important to be sown and gleaned. In that sense, everybody is a magic person and the person next to you on the bus definitely is Quan Shi Yin, even if appearing in what Mother Theresa would have called "a distressing disguise".
Outside the Four Grades
The safest course is to remain powerfully aware of one's bombu nature and learn from every opportunity. This is even more important for the teacher than for the disciple. As Trungpa used to say, the teacher is also a student. In fact, there is some truth in the notion that what the teacher teaches, and does so mainly by example, is how to go on learning. The more you understand the more you realise how much you do not understand, how vast are the possibilities and how fathomless are the imponderables. In this sense the teacher lives in shunyata, vast emptiness in all directions, but that vast emptiness is also innumerable Buddhas. Amitabha comes especially for bombu beings such as ourselves and our gratitude knows no bounds.
There is an original meaning of the term bombu as somebody who is not irreversible. A bombu is a practitioner who is not an arhat, non-returner, once returner, or stream entrant. In accepting our bombu nature, therefore, we are giving up complacency. There is here a profound paradox. When we genuinely and completely accept that we are in a totally vulnerable state spiritually, that is exactly the moment that we are grasped by Amida never to be relinquished. This is the eruption of other power at the point of abandonment of self power, which is the central mystery of Buddhism and the fundamental meaning of the Four Truths and all the other famous doctrines. Thus the person who fully takes himself to be "reversible" thereby become irreversible and the person who thinks himself irreversible is probably already falling back. All these ideas are worthy of contemplation, but it is best never to allow oneself to think that one has it all sorted out completely. Namo Buddhaya!