The answer to this question can be found in the rather lengthy afterward that the author provides us with at the end of the play which describes the future of the main characters after the curtain falls. In this afterward, Shaw seems to want to set the record straight about various misconceptions that audiences and people have come up with regarding the fate of his heroine. Note what Shaw says about the conclusions that people have reached after watching the play:
Nevertheless, people in all directions have assumed, for no other reason than that she became the heroine of a romance, that she must have married the hero of it. This is unbearable, not only because her little drama, if acted on such a thoughtless assumption, must be spoiled, but because the true sequel is patent to anyone with a sense of human nature in general, and of feminine instinct in particular.
Thus Shaw writes the afterward to this excellent play to combat the mistaken assumption that Eliza, as the obvious and impressive heroine of this play, would marry Professor Higgins as its hero. However, according to him, such a view clearly shows a mistaken understanding of her character and the play as a whole, as if you understand the characters carefully, you would never come to such a conclusion. Most amusingly, Shaw argues that Higgins would never marry because the most important woman to him in his life is his mother, who could never be replaced.