Lawrence's treatment of marriage in The Rainbow can be read as anti-patriarchal. The three generations of Brangwens we meet in the novel each struggle with marriage in different ways, but in every case the issue has to due with the social requirements of marriage, sexual attraction, and personal freedom. Lawrence can be thought of as anti-patriarchal in the sense that he values personal freedom, and in particular, the freedom to love as one chooses.
Tom Brangwen's marriage to Lydia is an example of marriage as a totalizing social force. Tom as a student feels the stirrings of creativity inside, but is unable to articulate them. Tom marries Lydia because he feels he needs a wife, and has some dull expectation of being in love and sexual fulfillment, but his hopes for the marriage are thwarted by Lydia's cultural differences and imperfect English.
Anna and Will, the second couple, see marriage as a kind of fantasy refuge from reality. Their relationship as lovers comes into conflict with the reality of having children; Anna's responsibilities as a mother, as contrasted with Will's relative irresponsibility, highlight how marriage can be different for men and women.
The third couple, Ursula and Anton, have a passionate romance that ends when Ursula turns down Anton's marriage proposal, preferring instead to be a free woman. She comes to realize, however, that her loneliness when Anton leaves is too high a price to pay.
The book can be seen as anti-patriarchal in that it sees true marriage as emotionally fulfilling and freeing for both men and women. Although the novel ends with Ursula writing to Anton to return, she does so not out of guilt in turning him down or economic necessity but because she has learned that her love for him is emotionally nourishing.