The theme is suggested by the allusion in the title: Eliza's self-realization as a human being and Higgins' difficulty in accepting that. This is clearer in the original play than in the 1938 movie or subsequent adaptations like My Fair Lady, which add considerable subsidiary elements. Eliza's desire to better herself socio-economically is only the setup, and is soon forgotten. Her worry later on of what is to become of her has an economic element, but it's not a social class rise question.