In Shaw's Pygmalion (and My Fair Lady), Professor Henry Higgins wants Eliza Doolittle to return to Wimpole Street for three intertwined reasons:
Eliza is his masterpiece—proof that phonetics can transcend class. Her success validates his life's work. He needs her to complete the ambassador's garden party test.
Higgins has grown dependent on her presence—her competence managing his household, her sharp mind, her challenge to his arrogance. He calls her "a tower of strength" but cannot articulate affection.
He mistreated her (called her "baggage," "squashed cabbage leaf"). Her departure exposes his vulnerability. Returning restores his controlled environment—and lets him avoid confronting his feelings.
She returns on her terms—not as pupil, but as colleague/friend. The play ends with her asserting independence; the musical hints at romance. Shaw's sequel (What Happened Afterwards) has her marry Freddy and run a flower shop—Higgins remains a bullying bachelor.