Professor Higgins objectifies Eliza as the main component of his experiment, even bullying her at times.

When Eliza takes a taxi and comes to Higgins for speech lessons so that she can "be a lady in a flower shop stead of sellin at the corner of Tottenham Court Road," (Act II) Higgins speaks about her to Pickering as though she is not a real person. 

HIGGINS. Pickering, shall we ask this baggage to sit down, or shall we throw her out of the window? (Act II)

After saying things that hurt Eliza's feelings because he speaks of her as a mere object, such as his proposal to Pickering that he can make a "duchess out of a guttersnipe," Higgins calls her ungrateful. Even when Pickering scolds his friend, asking him if he does not think the girl has feelings, Higgins callously replies, 

HIGGINS. Oh, no. I don't think so. Not any feeling that we need bother about. (Act II)

Having thus dismissed Eliza's feelings, Higgins returns to concentrating on what he considers essential; namely, her grammar is atrocious and will be harder to correct than her pronunciation.

So often, he is guilty of this domineering superiority. Throughout the later acts, when Eliza becomes angry after he has gone too far with his impetuous bullying, Higgins employs coaxing cleverness rather than an apology to subdue her. It is only when Eliza takes a stand for her own dignity after the ambassador's party that Higgins begins to perceive Eliza no longer as a sort of millstone around his neck, but as a person who is deserving of his admiration. 

In the play Pygmalion, Professor Henry Higgins is a pragmatic professor of phonetics.  His sole "joy" in life is the study of linguistics and how it impacts human interaction.

He treats Eliza Doolittle as a component of an experiment. He is rude and short-tempered with her.  His impatience is not directed at anything she does or does not do, but at her mere mortality.  The agreement to tutor her is not so much to help her as it is to win a bet concerning his abilities.

He is successful in changing her dialect.  However, her attitude is also changed. In the process, she takes on the professor's attitude and that proves to be her undoing.

Though she is grateful for his time and energy, she can not tolerate his abysmal intolerance of humanity and eventually leaves his home.