I know the story of Pygmalion. I have read the original 1913 version by George Bernard Shaw; and I have also seen Alan J. Lerner and Frederick Loewe's 1956 musical, My Fair Lady, directed as a movie in 1964 by George Cukor, before. However, only after reading the play Pygmalion, watching the 1938 film by the same name, directed by Anthony Asquith and Leslie Howard, and then watching the musical My Fair Lady back to back did I have my doubts about Henry Higgins' sexuality.
There are many similarities among the versions; in fact many of the lines written and spoken are exactly the same. Similarities can be seen in the dialogue exchanged between Eliza and Henry. However, there was one difference in the musical version of My Fair Lady that stuck me as odd, and that was how strongly Henry Higgins is against the women of the world. The assertions--"I prefer a new edition of the Spanish Inquisition" or "I'd be equally as willing for a dentist to be drilling than to ever let a women in my life"--are quite strong statements against women.
I am aware the Shaw never intended for Pygmalion to be a love story, so I am fairly certain that he never intended for it to become a source of political and social controversy on the topic of gays. My Fair Lady was created by Alan J. Lerner in cooperation with Frederick Loewe. I do not know anything about these gentlemen, but they must have had their reasons for making Henry Higgins, played by Rex Harrison, so adamantly against women. What was the point of this? Was it to illustrate that he was a confirmed bachelor? If so, then how is that fact important to the musical? Other than just giving My Fair Lady another catchy song and another crack at Best Musical Scoring, for which it won an Academy Award, it does not seem to me as relevant information. In fact, it appears contradictory of Higgins when he does decide to have Eliza in his life in the end.
At the end of the musical, Eliza returns to Henry. Presumably Eliza realizes that she has feelings for Henry and has a desire to live her life with him. It is safe to assume this, for there are no other discernible reasons that Eliza would want to return (unless she is simply a masochist). Therefore, some sort of show of affection would be appropriate; but Eliza does not receive a kiss, hug, or even a hearty handshake; instead, she is commanded to look for Henry's slippers. This action tells me that Henry is not interested in Eliza as a woman, but more of as a companion. It is my conclusion that Henry Higgins is indeed gay and that he wants Eliza as a female companion, or "fag-hag," if you will.
It is interesting because the play Pygmalion and the 1938 movie, produced by Gabriel Pascal, gave no indication of Henry's sexuality. I am guessing that My Fair Lady chose a homosexual Henry, who runs about his home singing and proclaiming (so ferociously his distaste for women), so that his character would better fit in with the gay musical theme of the film.