Shaw's Pygmalion is based on the tale of "Pygmalion" the sculptor in Ovid's (Roman poet) Metamorphoses, which is fifteen tales written in Latin in heroic hexameter. In Ovid's "Pygmalion," the sculptor creates a statue and calls her Galatea, then calls upon the goddess Venus, the goddess of Love, to bring her to life so he might wed her. In Ovid's story, as stated by Shaw in the "Sequel" of Pygmalion, Galatea can never fully overcomes the barrier between herself and Pygmalion, feeling that he is godlike and in some ways unlike her.
Shaw applies this Ovidian point to his play and prohibits Liza from becoming romantically attached to Higgins even though, as Shaw says, that while "Eliza's instinct tells her not to marry Higgins. It does not tell her to give him up." Shaw is suggesting that to be true to his source, Ovid's "Pygmalion," he has to keep a barrier between Liza and Higgins, and the barrier must in time demonstrate some of the friction and some of the same sort of dislike as exists between Ovid's Galatea and Pygmalion.
Shaw accomplishes this by having Higgins about twenty years older than Liza; by making him an unquestionable bachelor; by providing an "irresistible rival in his mother ... who has intelligence, personal grace, dignity of character without harshness, and a cultivated sense of the best art ... to make her house beautiful"; by making him ill-temperedly brusque and rude. On top of which, he gives Liza a sufficiently deprived and constricted background so that she is unable to understand Higgins words when he sincerely addresses her about (1) equality of address to persons and (2) his affection and respect for her
(Act V: "You call me a brute because you couldnt buy a claim on me by fetching my slippers and finding my spectacles. ... I think a woman fetching a man's slippers is a disgusting sight ... If you come back, come back for the sake of good fellowship; ... .").
Therefore, she goes all her days--though remaining attached to and dependent on Higgins (and Pickering) for affection and advice--believing in her own opinion of Higgins (which is that he has no respect and only wants her to fetch his slippers and find his glasses) and quarreling with him to the point that Pickering must ask her to be a little more gentle with Higgins. In this way, Shaw relates the "Sequel" to Ovid's story of Galatea and Pygmalion.