Quote 1
MRS. HIGGINS. Be quiet, Henry. Colonel Pickering: don't you realize that when Eliza walked into Wimpole Street, something walked in with her?
[…]
PICKERING. But what?
MRS. HIGGINS [unconsciously dating herself by the word] A problem. […]
MRS. HIGGINS. No, you two infinitely stupid male creatures: the problem of what is to be done with her afterwards.
HIGGINS. I don't see anything in that. She can go her own way, with all the advantages I have given her. (3.248-255)
Mrs. Higgins is concerned that her son and Pickering have been short-sighted, and failed to acknowledge the full extent of their task. Eliza's problems, like her personality, are multifaceted.
Quote 2
MRS. HIGGINS. You silly boy, of course she's not presentable. She's a triumph of your art and of her dressmaker's; but if you suppose for a moment that she doesn't give herself away in every sentence she utters, you must be perfectly cracked about her. (3.203)
Mrs. Higgins, like Mrs. Pearce, seems to agree that Higgins can get carried where his "art" is concerned. He seems unable to acknowledge how artificial Eliza's behavior is.
Quote 3
MRS. HIGGINS. You certainly are a pretty pair of babies, playing with your live doll.
HIGGINS. Playing! The hardest job I ever tackled: make no mistake about that, mother. But you have no idea how frightfully interesting it is to take a human being and change her into a quite different human being by creating a new speech for her. It's filling up the deepest gulf that separates class from class and soul from soul. (3.223-224)
Higgins considers his teaching to be a kind of social work. The inability to communicate, he suggests, is at the bottom of man's social issues.