She says "My character is the same to me as any other lady's".
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Higgins thinks he's pretty good at pinpointing accents. He figures he can not only tell their origins but also their socio-economic class. Remember class structure was more rigid than limestone in England. Liza and her flower selling become the catalyst for the story. Liza, obviously of low class presents the challenge. Can Higgins train her to sound like nobility, borne and bred? There is, of course, more to Liza than her accent which is one of the major themes of the play. She eventually shows herself to not only master an accent but have a keen understanding of social norms, so much that she can manipulate the manipulators.