Is Jesus a false prophet?
I don’t envy the town leaders of Capernaum. Quite likely, they were under pressure from the Jerusalem religious authorities to deal with Jesus.
Given Jesus’ pronouncement of doom against Capernaum, Chorazin, and Bethsaida (Luke 10:13-15), the logical conclusion is that these towns rejected Jesus — but without going so far as to arrest him.
Now Jesus’ experience had its share of conflict. He had even been asked to leave a town before this. And people come and go around Jesus without “doom.”
There is no record of eviction, and it seems unlikely that the town leaders could reach consensus if the synagogue ruler Jairus or local businessman Zebedee were influencers. (Analogous to the presence of Nicodemus and Gamaliel in the Sanhedrin.)
I take it, however, that there was some sort of majority rejection among the leaders to preserve the standing of their communities.
After all, if Jesus wasn’t a political Messiah, what did the political leaders really stand to gain from his activity? Contrast that against what they stood to lose if people listened to Jesus’ criticism.