The quarrel with Samaria was seven centuries old and still bleeding. After Assyria resettled the north, the population that emerged there kept only the five books of Moses and worshipped on Mount Gerizim rather than in Jerusalem. They built a temple there; a Jewish ruler, John Hyrcanus, destroyed it around 128 BC. When the woman says our fathers worshipped on this mountain, she is standing in its shadow.
The well is a real, identifiable site and it is deep — well over a hundred feet — which is exactly why the woman points out that Jesus has nothing to draw with. Drawing water was women's work done in company at dawn or dusk; a woman coming alone at the sixth hour, the heat of the middle of the day, was avoiding other women.
Two social rules are broken at once. A Jewish teacher did not hold a public conversation with a woman he did not know, and a Jew did not share a drinking vessel with a Samaritan. The disciples' reaction when they return — they marvelled that he was talking with a woman, and nobody dared ask why — records the shock.
The second half moves to a royal official, a man in the service of Herod Antipas, whose son lies ill at Capernaum about twenty miles from Cana. The distance matters: he asks Jesus to come down, is told to go, and later matches the hour of the healing to the hour of the word. That check is the point of the story.