What lessons has Pickering taught Eliza that Higgins could not teach her?

In Act V, Eliza comes downstairs looking self-possessed and very much at home. She uses the genteel accents that Higgins has taught her. Higgins is furious and claims that he has made her what she is. Pickering assures Eliza that he does not think of her as just an experiment, and she expresses her gratitude to him for everything, especially for teaching manners to her. She adds pointedly says that Higgins could not have taught her such manners.