In Act 3 of Pygmalion, describe the relationship between Mrs. Higgins and her son.
We understand that Higgins is both a bully and a rather crusty bachelor. He doesn't believe that about himself at all, but his mother sides with us. In fact, when he shows up at her house in this scene, the first words she says to him are:
"What are you doing here to-day? It is my at-home day: you promised not to come.... Go home at once.... I'm serious, Henry. You offend all my friends: they stop coming whenever they meet you."
She's right, of course. He has none of the social graces his mother has--and which he's presumably trying to teach Eliza. She really does want him to leave, though she is more distressed than angry.
It turns out Henry would like to use his mother's at-home day as a practice session for his pupil. When he tells her he's bringing over a girl, Mrs. Higgins is thrilled--that perhaps someone else will have a positive influence on her son's hopeless behaviors. Alas. It's only a kerbstone flowergirl. The event is a moderate success, and Mrs. Higgins is charmed enough by Eliza to forgive Henry's lapses in social courtesy.
Their relationship is humorous and good-hearted, as they banter about all manner of things (no pun intended). Each of them is serious about their issues, but together theirs is a good-natured give-and-take which the audience generally finds amusing.