The tale of Pygmalion is an adaptation of the Roman legend of Pygmalion the sculptor found in Ovid's work Metamorphosis and, as Shaw mentions at the end of the Epilogue of Pygmalion, Galatea (the "flower girl" of Ovid's tale who was actually a sculpture brought to life) never does come to really like Pygmalion, according to Shaw, because he is too aloof and cold in a god-like fashion. Since Shaw is following this model, no truce is ever really called between Higgins and Liza, even though the real possibility of it develops in Act V prior to Eliza's reluctant departure to attend her father's wedding.
In this act, Higgins shows real sincerity and genuine feeling and rather eloquently tells Liza what he thinks of her, while nonetheless insisting that his behavior is fixed and unchangeable ("I cant change my nature; and I don't intend to change my manners"). However, Liza misses the import of Higgins' words ("I think a woman fetching a man's slippers is a disgusting sight") and insists that his view of her is that she is lowly and a convenient service for slipper-fetching.
Since she and Higgins can't come to any amenable resolution between them, and since Liza declares she doesn't want love from Higgins of the sort that Freddy gives her ("I want a little kindness. ... we were pleasant together and I come--came--to care for you ... but more friendly like"), Liza will want to marry someone else. Being young and lovely and being pursued ardently by Freddy, despite the fact that he is incompetent because his mother couldn't afford his education (or wouldn't?), Liza marries him. In addition, Higgins' callousness and refusal to offer a recanting apology of the fashion Pickering offered causes Liza to decline to resume her residence on Wimpole Street, which eliminates the possibilities of Higgins finding a Duke or Earl to propose to his "Duchess."