Almost all of my friends who watched Silence before me left the movie with some big questions regarding the ending, so when I first watched it, I had already formed the opinion that I needed to pay close attention to what went on, especially toward the end of the movie. Those who have seen the movie know that the ending, is deeply unsettling, because it seems that ultimately, after watching so many instances of heroic faith, the solution proposed is to feign apostacy and hope for the best.
The more obvious answer seems to be that Fr. Rodrigues (Andrew Garfield) and Fr. Ferreira (Liam Neeson) did the right thing. As the Inquisitor (Issey Ogatta) points out in one of his discussions with Fr. Rodrigues, Japan is a swamp and the tree of Christianity cannot grow there, at least not unless it mutates. The actions of Fr. Rodrigues and Fr. Ferreira before him, then, are simply what needed to be done. They denied Christ early and often outwardly, but confessed Him inwardly and quite likely were able to minister others who did the same.
Intuitively, however, this explanation leaves something to be desired. If the real solution was to pretend apostasy, how do we square that with the many Japanese Christians whose horrific suffering and heroic perseverance we see almost throughout the movie? In addition, it is unpalatable to accept that Christianity could not take root in Japan as it did elsewhere, even amid persecution.
Not only do I think that it is incompatible with the Christian Tradition to accept the idea that one can deny the faith publicly but confess it inwardly--to be an "incognito" Christian of sorts--but I do not think the point of the movie is to portray the choice of Fr. Rodrigues in a positive light. For me, the first clue as to why this is not the case was finding out that the author of the novel by the same name--which, admittedly, I have not read--was a Roman Catholic Japanese man. The notion that the many brutal murders of Japanese Christians which are portrayed throughout the movie were somehow seen as unnecessary by a fellow Christian does not seem likely to me. Second, there are a few lines in the movie which seem to push one toward a different interpretation.
First, when Fr. Rodrigues is brought to the Inquisitor's compound, he is introduced to the Interpreter (Tadanobu Asano), who informs the former that he learned Portuguese from previous Portuguese Jesuits, who made no greater effort to learn Japanese than a limp "Arigato," and more than trying to serve the Christians, thought themselves superior to them. Fr. Rodrigues denies that he is anything like them, in Portuguese. At the end of the interaction, the Interpreter tells one of the guards that Fr. Rodrigues is arrogant and will break eventually.
In another interaction, Fr. Rodrigues asks if he will be tortured to death, like the many clerics who were killed when the persecution started. The Inquisitor's response is rather striking. He says that he has learned better than to repeat that mistake. Apparently, the murders—even on such a massive scale—served only to strengthen the resolve of the remaining Christians. Instead, the Inquisitor's plan has shifted to pushing the priests to apostatize in order to demoralize the faithful. In fact, the previous apostate priest, Fr. Ferreira, has been tasked with writing a book which shows the errors of the Christian faith and why it is unnecessary in Japan. Such a book would be a great spiritual wound to the Japanese Christian community. The Inquisitor's strategy, thus, is as cunning as it is evil. He means to torture his Christian captives in front of Fr. Rodrigues—in the meantime reminding him early and often that the Japanese Christians are no true believers, that they're really accepting all this suffering for his sake—to push him to apostatize for their sake.
Eventually, Fr. Rodrigues wakes up one night to the sounds of screaming and what sounds like snoring. He screams to notify the guards that someone is in pain while one of guards is fast asleep. Fr. Ferreira notifies him, however, that this is not the case. Five of the Christians have been suspended upside down and given a small cut on their necks so they would not die quickly. What sounds like snoring is in fact the sound of the Christians slowly suffocating in their own spit and blood. Fr. Ferreira then reminds Fr. Rodrigues that all this suffering is happening for his sake. He berates him on the fact that he has undoubtedly associated his own suffering with Christ's in Gethsemane, pointing out that this is nothing short of arrogance. Fr. Rodrigues must apostatize, for their sakes. A defeated Fr. Rodrigues does not put up a fight, so he is brought out of his cell and an icon of Christ the Bridegroom is placed before him, but just at the last minute, he hesitates. Fr. Ferreira then utters the most crucial line in the whole movie. "You are about to commit the most painful act of love," he says. To a Christian—at least in retrospect—this line is pregnant with meaning. We are meant to see the last night in Fr. Rodrigues' cell as a new kind of Gethsemane and his eventual apostasy as a new Crucifixion, except that whereas the former one was a real agony and the real Crucifixion, this one is only a delusional one.
To a Christian, the idea that anything they do could be classified as "the most painful act of love" is simply impossible. The most painful act of love was the one committed by the Incarnate Lord, who voluntarily accepted to die so that we might have life. That Fr. Rodrigues truly believes that he is doing anything even remotely approaching that shows that deep inside him pride has taken root.
In fact, it seems that the message of the movie is to warn against a romanticized view of what mission work entails. Fr. Rodrigues and Fr. Garrupe (Adam Driver) seem shocked by the state of the Church in Japan. They find a local population that is deeply faithful, but—for the most part—has a basic grasp of the faith at best, which is somehow different than what they expected. Where one might expect paternal correction coming from love, Fr. Rodrigues responds with indifference and Fr. Garrupe—at least initially—responds with frustration. Of course, it is unclear how Fr. Garrupe's relationship develops, after the two priests separate we see him only once, on the occasion of his dying trying to hold up one of the Christians who are being drowned in order to push him to apostatize.
Fr. Rodrigues, on the other hand, begins to internalize the idea that the Christian faithful in Japan are dying en masse for him, not Christ. He conflates their lacking theological knowledge with faith in God and thus presumes that what he does when he apostatizes is really saving the Japanese from themselves, since as the Inquisitor says, Japan is a swamp, or as Fr. Ferreira points out, the Japanese are just too dumb to understand Christianity. In other words, Fr. Rodrigues--and Fr. Ferreira before him--really think they are better than the Japanese Christians, despite the fact that the faith of the former has been confirmed by the countless suffering they undergo with frightful frequency. So, Fr. Rodrigues chooses to apostatize and, presumably, faithful Japanese Christians continue to pay the ultimate price for their faith.
I do not think the last scene of the movie contradicts this interpretation. We are clearly supposed to see that Fr. Rodrigues believes inwardly, but he has failed to confess Christ with his lips (cf. Rom. 10:9). He has tried to be an incognito Christian for much of his life, but at the end, the small wooden crucifix which one of the Japanese Christians gives him on his way to be martyred is merely consigned to the flames of a Buddhist burial.