Symbolism, Imagery, Allegory
The Magistrate Inoue uses the idea of marriage to illustrate Japan's relationship to the West. Because why not?
The Four Mistresses
First, Inoue tells the story of a Japanese monarch forced to choose between his four mistresses. Each mistress wants the man for himself and "constantly quarreled out of jealousy" (7.5)—it's basically an episode of The Bachelor. But here's the thing: Inoue is actually talking politics. The king represents Japan, while the four mistresses represent Portugal, England, Spain, and Holland.
Like those four mistresses, Portugal, England, Spain, and Holland each want Japan all for themselves. Instead of marriage, however, these countries are looking for moolah—lucrative trade contracts, political alliances, and all that kind of thing. Just as it's wiser to dump all the mistresses because they've all proven themselves to be shady ladies, it's better for Japan to cut off contact with the West than be forced into an uncertain political situation.
The Ugly Woman
But Rodrigues doesn't represent any country—he represents the Catholic Church. As it turns out, Inoue has a metaphor for that, too. He calls the Church an uggo, likening its missionary work to "the persistent affection of an ugly woman" (7.28). Ouch, that's harsh. What's more, the Church is a "barren woman" (7.28)—in other words, it has nothing to offer the Japanese government in political or financial terms.
When dealing with countries, Japan has at least the potential to gain something from the relationship: a trading partner or military ally could be valuable indeed. As for the Church, however, all she can offer is a permanent pain in the neck, in the form of domestic uprisings like the Shimabara Rebellion and foreign interlopers like Father Rodrigues.