What does Luke 10:12 mean?
To carry Jesus' message into surrounding villages and towns, seventy-two followers receive His instructions. If the townspeople reject His message, the commissioned messengers are to go to a public place, shake the dirt off their feet, and announce that the kingdom of God will come with judgment (Luke 10:1–11). The eternal judgment is severe (Zephaniah 1:14–18). "That day" is the "day of the Lord" when God will remove rebellious people from His presence for eternity, much like the dust falling from the disciples' feet.Though short, this verse includes details which can become distracting.
Sodom's characteristic sin, traditionally, was sexual immorality. Besides the story of Lot (Genesis 19:1–29), this sin is mentioned in Jude 1:7, the non-canonical Book of Jubilees, and the writings of the Jewish philosopher Philo. In this context, however, coming right after a promise of judgment on towns that reject Jesus' disciples, Jesus is most likely referring to arrogance that made them unafraid of judgment (Ezekiel 16:49). The angels came to Sodom to rescue Lot, a man of peace (Luke 10:5–6) but the rest of the city refused to show them a proper welcome.
The second theological implication is the phrase "more bearable on that day." "That day" refers to the coming of the kingdom of God. Here, it specifically means the day of judgment. Salvation is a yes-or-no condition; either you are saved and you are going to heaven, or you are not saved and you are going to hell (John 3:16–18, 36). "More bearable" seems to say that there are different levels of punishment in hell. This is a common aspect of cultural depictions of hell, most famously The Divine Comedy by Dante. However, the basic idea is affirmed in Scripture (Revelation 20:11–15). Every person who is not saved will meet God's judgment at the Great White Throne. The sheep and goats will have already been separated, so the judgment doesn't determine if these people will go to hell. Instead, Jesus opens books and "the dead [are] judged by what was written in the books, according to what they [have] done" (Revelation 20:12). Based on this, it appears eternity holds different levels of punishment depending on a person's choices in life (John 19:11).
Why, then, would the people of infamously depraved Sodom experience less torture than these towns? In His parable exhorting the Twelve to be ready for His second coming, Jesus says, "And that servant who knew his master's will but did not get ready or act according to his will, will receive a severe beating. But the one who did not know, and did what deserved a beating, will receive a light beating. Everyone to whom much was given, of him much will be required, and from him to whom they entrusted much, they will demand the more" (Luke 12:47–48). Towns during Jesus' earthly ministry experienced power and preaching more than others. If the people in those towns refuse to repent, they will be judged more harshly than the people of Sodom who sinned egregiously but had a less-direct opportunity to hear the truth.
That doesn't mean Sodom is not culpable. Romans 1:18–23 explains that God displays His "invisible attributes, namely, his eternal power and divine nature" in His creation. Even so, Sodom—like every other person who did not receive special revelation from God—rebelled against what little they knew and worshiped creation instead of the Creator. That choice alone condemned them.
Jesus goes on to compare cities He ministered to with those He didn't. Chorazin and Bethsaida, in Galilee, witnessed Jesus' power and teaching first-hand, yet did not repent. If Jesus had given such signs to Tyre and Sidon, the Gentiles there would have mourned their sins and begged for forgiveness (Luke 10:13–14). Capernaum, too, is judged (Luke 10:15). Matthew's account compares Sodom to Capernaum (Matthew 11:23–24). It's a sober warning that the city in which Jesus ministered most will be judged more harshly than the city held as the pinnacle of sinfulness.