Aside from my distaste for such a technical reason for selecting haftarot, here it also ignores the simple meaning of the verse; especially since Amos directs his words specifically to the Northern Kingdom (when Joseph was sold by all the brothers, and certainly not by Ephraim, the tribe that usually represents that kingdom), Amos seems to be complaining about their putting money above treating other people properly.
Further in the haftarah, the prophet speaks in God's Name, noting that it was God who got the Jews past the Emorites, took them out of Egypt, helped them survive forty years in the desert, and gave them the Land. It was also God who set up prophets and Nazirites (people who vowed to forgo wine, haircuts, and contact with corpse impurity for a certain period of time). Instead of being grateful, the Jews forbade prophecy and fed the Nazirites wine (luring or forcing them into violating their oath).
The prophet devotes several verses to this issue, suggesting that he understood God to "care" more about the Jews' failure to heed the warnings sent them than the sins themselves. Sin is understandable and comes to us all, but shutting out the voices that could help us improve is less excusable.
That also explains the punishment, that each person will lose that quality he or she would ordinarily have relied on to save him from adversity, the swift will lose his speed, the strong his strength, the hero his courage, the archer his ability to stand, and so on. Our strengths fooled us into ignoring the warnings of the prophets; losing them will teach us the lesson we need to learn.
Correlations, Connections, and Prophets
The second half of the haftarah takes a turn that will eventually lead back to the focus on the prophets we identified in the first half. Amos notes that God has "known" only us of all nations, and that "knowing" is a necessary precursor to two people walking together. This connection leads him to note other connected events, which then allow for expected results, as in the various metaphors Amos trots out.
When a lion roars, it means he has caught his prey; when a bird falls suddenly to the ground, it's been caught in a trap; when a trap springs, it means it has caught something; when alarms are sounded in the city, it signifies a time of danger. Note that all the cases involve capture or hunting, and Amos is pointing out the well-known signals of those outcomes.
In what is meant to be a similar way, the "knowing" that God speaks of in terms of the Jewish people takes the form of God not acting without informing the Prophets; their words, then, are to be seen as just as much part of a chain as the lion's roar. The people's refusal to heed those warnings is thus the first, and crucial, step in leading to their downfall, and thus the one to be most bemoaned.
Looking back to the Torah reading, the haftarah seems to argue that the brothers' fatal error was not the sale of Joseph itself, but their rejecting his dreams. Distasteful as they found the idea of his ruling over them, the dream was an accurate prediction. The desire to run away from truth can be strong, but the Torah reading and the selection from Amos warn us to resist it. Truth comes to us in many forms, and if we heed it, we can know which challenges we face, can consider how best to cope with them, and come out as well as possible. If we reject the truth or stifle its messenger, none of that can happen.
Famous Verses and Their Echoes
The first verse of the haftarah—"for three sins of Israel, and for the fourth I will not allow him back"—is recorded by Maimonides in the Laws of Repentance 3:1. Based on statements at the end of the Talmudic tractate Yoma, he codifies the principle that God does not count the first three times one commits a certain sin, only counting from the fourth on.
In context, Amos seems to have been referring to four different sins; it was the fourth type of sin that was intolerable to God in the original, not the fourth incident. When the Sages understood the verse the other way, they assumed the issue was the extent to which a person or nation is enmeshed in sin; at the national level, that might reveal itself in the range of sins committed, but for the individual, it is the repetitiveness of sin that best shows the person has lost the battle, and is now captive to that sin.
That same verse leads Mabit (R. Moses ben Joseph Trani, 16th Century Safed, Rabbi of the community after R. Joseph Caro’s death) to raise the question of the definition of tzaddik, a righteous person. He notes that God is referred to that way, Noah, Joseph here (following the tradition that the verse refers to the sale of Joseph), and the entire Jewish people. The word is not uni-dimensional, nor does it have one clear definition. Each time we see the word in Scripture, we might productively question how it is being used, the kind of righteousness being lauded.
At the end of the Laws of Nazirites, Maimonides notes that 2:12's connecting Nazirites to prophets shows us that such vows are properly undertaken only for the purpose of becoming holier and closer to God.
Finally, the last verse of our haftarah uses the striking metaphor of "the lion has roared, who will not fear?" as the lead-in to pointing out that when God speaks, prophets cannot but issue their prophecies.
In the Responsa literature, this phrasing is also sometimes used to express trepidation about disputing earlier authorities. For one example, the 18th century R. Ezekiel Landau disagrees with the 13th-century Torah giant Rashba in one of his responsa (Noda BiYehuda, Later Responsa, Yoreh Deah 56); he has Ran, who lived close to Rashba chronologically, for support, but cites our phrase to express his trepidation at taking on this giant.
In summary, then, Amos reminds us that we often ignore the prophets because we rely on our own strengths. So, too, Joseph's brothers insisted on denying his dreams, which could have told them the future that was coming their way.