This prophecy is structured as a pattern where Hashem addresses nation by nation with the infamous rebuke of, “For the three sins of [name of nation] I can forgive but for the fourth sin I cannot forgive.” The first six recitals of this reproach are only a prelude to the two main ones which come in chapter 2 and are directed at Yehuda and Yisrael. Amos, like Yeshaya his student, is a universal prophet and is Hashem's messenger to the nations of the world as well as to Bnei Yisrael. However, his primary objective is to bring God’s chosen people, Bnei Yisrael, to repent from their evil ways.
There is discussion among the commentators as to the identity of the three forgivable sins. Metzudas David explains that they are the three cardinal sins and that the fourth sin is only to rubber stamp the already impending punishment. Rashi and Radak are of the opinion that God, due to His compassionate ways, is willing to forgive the first three sins, whatever they may be, however, the fourth sin is one step too far for Him to forgive. What is the exact nature of this ‘fourth sin’ that it causes such severe calamities to befall its perpetrator? Perhaps the answer to this is the word אכזריות (cruelty).
All eight peoples spoken about here committed different sins (with perhaps the exception of Azza and Tzur) but all invoke the same explosive reaction from Hashem. This is because Hashem is not looking at the externalities of these sins, but He is punishing them for what motivated all of them to sin. The root of all these sins is the same; cruelty. אכזריות is the unreserved cruelty in which man displays his inhumane capability to destroy in the most gruesome ways. In a world full of diversity, where each race struggles to overcome its competitors, conflict, war and even cruelty is understandable. But אכזריות is when man goes beyond this and brutally inflicts horrors to rob another person of his basic human dignity. Hashem cannot allow this to go unpunished, as it is a direct threat to the very existence of His world.
If we take a look at the ‘fourth sin’ of each nation, it is blatantly obvious how it oversteps the label of cruelty and enters into the far more sinister realm of אכזריות. To ‘plough’ fellow men like one ploughs a field using instruments with metal spikes is not warfare, it is אכזריות. To hunt down and capture the few remaining escapees of a terrible exile, to split open the wombs of pregnant women just to gain a meagre bit of land, to burn to dust the bones of royalty are all not warfare; they are אכזריות. In all these cases, it is the supposed elevation of man which has been utterly debased and replaced by the mostly lowly of animalistic behavior. Therefore, even though Hashem is willing to forgive, time after time, even the worst of sins, when it comes to אכזריות, Hashem has no choice but to blot it out and hence, “But for the fourth, I cannot forgive.”