Henry Higgins isn't quite the misogynist we think he is. Neither is George Bernard Shaw, the writer of Pygmalion, even though Higgins seems at times to be speaking with Shaw's voice.
Shaw was a democratic socialist, and he wrote his plays as social and political commentary, not for entertainment. Pygmalion, for example, deals with the rigid class structure of British society and is only incidentally about womens' rights.
Shaw was pro-women and supported equal rights and the suffragette movement, although at first glance Higgins's lines would seem to contradict that.
Shaw believed that women were no less the unwilling victims of a male capitalist society than the people of Britain as a whole, that marriage for financial security was simply a legalized form of prostitution, and that the conventional family was an artificial institution designed to reduce woman to the level of a possession—which is very much how Higgins first perceives and treats Eliza Doolittle.
At the point in the play from which these lines are taken, Higgins has offered to train Eliza (in her words) "to be a lady in a flower shop 'stead of selling at the corner of Tottenham Court Road," and the housekeeper, Mrs. Pearce, has taken Eliza off to have a bath—with "Monkey Brand," says Higgins, "if it won't come off any other way" (Monkey Brand soap was a highly abrasive soap used for household cleaning, not as a bath soap). Higgins is treating Eliza as a possession that he can do with as he chooses.
Higgins's views about women change significantly by the end of the play, however, and Eliza helps him to change, which is one of the themes of the play.
By teaching Eliza to be "a lady in a shop," Higgins wants to demonstrate that class distinction is merely a matter of talking and dressing according to society's standards and that the imposed class structure has nothing to do with the actual character of the person relegated either to a low or high standing, which he perceives as little more than a matter of chance. For Higgins, teaching Eliza how to be "a lady in a shop" is simply an exercise to prove how great he is at teaching people how to speak and act correctly in society. For Shaw, this same exercise serves to send a message about class distinction and the inequality of the sexes.
With this in mind, Higgins's little tirade about women —and equally about men, although the underlying sense of equality is lost in the rhetoric—is Shaw's attempt to show his audience that men and woman ought to be treated equally, and that neither sex should strive to dominate the other—either in society or in their own private relationships.