In Pygmalion what is it that Higgins learned from Eliza even though he was her teacher?

One might be tempted to say that the pig-headed Henry Higgins learned nothing from Eliza Doolittle, but that's not entirely true. While he continues to treat her rudely and orders her around as if she is his errand-girl, by the end of the play he has developed a grudging admiration for her newfound spunk. She is no longer afraid to fight back against him. He says, "I like you like this." He also praises her...

One might be tempted to say that the pig-headed Henry Higgins learned nothing from Eliza Doolittle, but that's not entirely true. While he continues to treat her rudely and orders her around as if she is his errand-girl, by the end of the play he has developed a grudging admiration for her newfound spunk. She is no longer afraid to fight back against him. He says, "I like you like this." He also praises her strength of character. He even tells her she is throwing herself away on Freddie, saying she could marry a king if she wanted.

Higgins also expresses surprise when Eliza informs him that she learned how to be a lady from Pickering's example, not from Higgins, indicating that Eliza's good opinion means something to him. 

In the end, Higgins has, in fact, brought a statue to life, as in the original Greek myth: Eliza becomes her own person, independent of her "creator." His behavior may not change, but he has possibly developed an awareness that Eliza is a human being, not just an experiment in linguistics.