But that just doesn't make sense to me!

I'm always interested in what does/does not make sense to people.

Recently we had a sermon on John 4, the woman at the well, in which the interaction between Jesus and the Samaritan woman was presented as a paradigm for evangelism.
That doesn't make sense to me.
Jesus draws attention to his own identity to reply to the womans rebuff
"If you knew who I was....." Should I do that?
Jesus bizarrely asks the woman to get her husband, then knows about her marital history.
Am I meant to have prophetic knowledge of peoples circumstances too?
Jesus kind of puts down the woman religious knowledge and practices. Should I do that too?
Jesus identified himself as the Christ. Should I do that too?

So I had to do a Bible study on same passage. I fear my Bible study made little to no sense to those who came along. Here are some points.

John 2-4 sees a similar movement to Acts 1:8. Jesus first goes to Jerusalem, then Judea, then Samaria, and then , in the form of the Samaritans confession and the imperial official, to the ends of the world. The disciples are drawn in for the harvest, but are reaping from what Jesus has worked.

The conflict is obvious from the beginning, Jesus is a Jew and the woman is a samaritan. What was the problem with Samaritans. Well the problem began way back in 1 Kings 12. The northern tribes split off from the south and Jereboam (from Shechem), their leader decides to set up temples other than the one in Jerusalem.

Eventaully the North is smashed for their idolatry by Assyria. In the place of the people, Assyria moves in other nations, with other Gods. Here is 2 Kings 17:29-33 ²⁹ Nevertheless, each national group made its own gods in the several towns where they settled, and set them up in the shrines the people of Samaria had made at the high places. ³⁰ The people from Babylon made Sukkoth Benoth, those from Kuthah made Nergal, and those from Hamath made Ashima; ³¹ the Avvites made Nibhaz and Tartak, and the Sepharvites burned their children in the fire as sacrifices to Adrammelek and Anammelek, the gods of Sepharvaim. ³² They worshiped the LORD, but they also appointed all sorts of their own people to officiate for them as priests in the shrines at the high places. ³³ They worshiped the LORD, but they also served their own gods in accordance with the customs of the nations from which they had been brought.

Note there are five groups listed, with their Gods.
In 2 Kings 18:34 there is a list of another 5 groups, with their God's who did not save Samaria.

Ezekiel, in the context of indicting Jerusalem as an adulterer, also mentions Samaria, and her restoration

⁵³ “‘However, I will restore the fortunes of Sodom and her daughters and of Samaria and her daughters, and your fortunes along with them, ⁵⁴ so that you may bear your disgrace and be ashamed of all you have done in giving them comfort. ⁵⁵ And your sisters, Sodom with her daughters and Samaria with her daughters, will return to what they were before; and you and your daughters will return to what you were before. ⁵⁶ You would not even mention your sister Sodom in the day of your pride, ⁵⁷ before your wickedness was uncovered. Even so, you are now scorned by the daughters of Edom^[a] and all her neighbors and the daughters of the Philistines—all those around you who despise you. ⁵⁸ You will bear the consequences of your lewdness and your detestable practices, declares the LORD.

⁵⁹ “‘This is what the Sovereign LORD says: I will deal with you as you deserve, because you have despised my oath by breaking the covenant. ⁶⁰ Yet I will remember the covenant I made with you in the days of your youth, and I will establish an everlasting covenant with you. ⁶¹ Then you will remember your ways and be ashamed when you receive your sisters, both those who are older than you and those who are younger. I will give them to you as daughters, but not on the basis of my covenant with you. ⁶² So I will establish my covenant with you, and you will know that I am the LORD. ⁶³ Then, when I make atonement for you for all you have done, you will remember and be ashamed and never again open your mouth because of your humiliation, declares the Sovereign LORD.’”

Note that Samaria is described also as an adulterous woman, and her restoration is to shame Jerusalem and is not on the basis of the covenant with Jerusalem.

All of Israel herself is spoken of as an adulterous wife to YHWH. Famously in the book of Hosea, but also in Isaiah 54:6 The LORD will call you back
as if you were a wife deserted and distressed in spirit—
a wife who married young,
only to be rejected,” says your God.
⁷ “For a brief moment I abandoned you,
but with deep compassion I will bring you back.
⁸ In a surge of anger
I hid my face from you for a moment,
but with everlasting kindness
I will have compassion on you,”
says the LORD your Redeemer.

And so it shouldn't too difficult to recognise in John 4 the biblical typescene of a betrothment.
All of our movies have fairly stock standard boy-meets-girl tropes, which are instantly recognisable to us.
The bible also has a pattern for how engagements happen.

1. The bridegroom is encouraged to leave his family (or kicked out) and journeys to a foreign land
2. He meets a girl at a well
3. Someone draws water from the well
4. He reveals his identity
5. The girl runs home to tell the family
6. They get married
7. Eventually he returns back to his family and is welcomed

Isaac and Rebekah(done for him) Genesis 24:12-21
Jacob and Rachel (the grandma of Samaria)Gen 29:1-12
Moses and Zipporah Exodus 2:15-22
Saul and Israel 1 Sam 9 (Saul messes with the story, instead of getting a wife (or the donkeys he is looking for), he meets a prophet, who tells him everything that is on his heart, calls him the ‘desire of all Israel’ and annoints him as Messiah.

Contextual factors point to a betrothal scene here too.
Jesus has just been described as 'the bridegroom' by John the baptist (3:29), which is also connected to Jesus' role as the Christ. Prior wedding language has also appeared in chapter 2, where Jesus assumes the duties of the bridegroom, though 'his time has not yet come'.

Jesus then, leaves his family, travels to a strange country, meets a woman at the well, reveals his identity, she runs back to tell the family (city) they come and rejoice, and then Jesus returns to his family and is welcomed there (even though a prophet is not welcome in his home town).

This is a betrothal scene. But the woman is not the bride, or, in a sense she is, in as much as she represents Samaria, and Jesus is YHWH/the Christ her bridegroom.
Jesus comes to Shechem, to Mt Gerazim, to the spiritual heartland of Samaria. To Jacobs field, to the well, to the stones of blessing and cursing from Deuteronomy.

And when he gets there he offers living water.
What is this living water and how is it connected to Jesus identity?
Jeremiah 17:13 speaks of YHWH himself as the living water. Psalms like Psalm 46 speak of a river of gladness that flows from the presence of YHWH in his Temple. Ezekiel 47 picks up similar imagery with a river that flows from beneath the right shoulder of the Temple, bringing life and abundance.
The living water comes from YHWH and his temple. Jesus has already described his body as the Temple. In John 7:37-39, the living water is the Holy Spirit, given after Jesus death. In John John 19:34, Jesus is pierced beneath the shoulder (his breast in one tradion 'his right breast', and blood and water flow from his side. In John 21, Jesus will supply the numerolgically significant 153 fish to the fisherman, as in Ezekiel 47 (See Richard Bauckham on Gematria and unity in John for this one).
The living water is Jesus' identity as YHWH and temple, able to give eschatological life, through the pouring out of the Spirit.
This explains the relativising of the worship sites of Mt Gerazim and Jerusalem. Worship is now centred around Jesus (the truth), empowered by the Spirit.

What of Jesus request for the woman to call her husband? How does this fit into the wider, symbolic reading of the woman?

A hint may be that the Hebrew word for husband and the Hebrew word for Baal (divine Lord/god) share the same root and are essentially the same word.
Samaria at this time has no Lord/Baal.
She has had five Baal's (remember the listing of five groups with their Gods?) and the Baal she has now isn't really hers.
I assume this last reference is to Samaritan worship of YHWH. He is not really Samaria's husband, for salvation comes from the Jews, and the Samaritans worship what they don't know.

The samaritans come to believe in Jesus however, so in one sense, the divine bridegroom does indeed get his bride. This is delayed though, until chapter 12. More are to be included in this bride. It is not until chapter 12, when greeks wish to see Jesus , that Jesus declares 'My time has come'

John's concern is to present Jesus as the bridegroom for Jews, Samaria and the entire world.
He is the source of the Spirit, that life giving water. He is the temple and so the centre of worship. He goes ahead of the disciples, sowing the seed of salvation, completing the work the Father sent him to do. The disciples simply reap the harvest.

Complicated, but make more sense to me.