is "shelved," we dig up an old debate. The ending of My Fair Lady (1964) is problematic.
The hero and the heroine argue about splitting up -and are so caustic to one another, they seem better off going their separate ways- but then they return to each other for no reason.
Eliza Doolittle (Audrey Hepburn) is a poor flower girl who wishes to speak well enough to raise her standard of living. A linguist, Professor Henry Higgins (Rex Harrison), takes on the challenge and teaches Eliza to speak and behave in a manner beyond her original goal of working in a flower shop. Higgins gets carried away and creates the appearance of a person who might be a duchess or a princess. 
The last big scene between the two of them discusses what should happen to Eliza after the experiment is over. Higgins insists that she cannot make her way in life without him since, "There's not an idea in your head nor a word in your mouth that I haven't put there."
Eliza counters with a rousing, triumphant song called "Without You." They part and Higgins is left to ponder his life without Eliza. But at the last second, Eliza makes her way back to his home, leaving us to infer that they do end up living together.
Why return? That Higgins is decidedly abusive and incorrigible is not a post-modern, presentistic reading of the material; he is meant to be, as Eliza calls him, "a brute." If she's thoroughly free of him why return? Harrison's Higgins is so aloof, there is no hint of a romance between them and there is no real friendship. It makes very little sense that Eliza would benefit from further contact with this man.
Reading the original Shaw material, one discovers that we are not meant to know her choice.The play ends ambiguously with Eliza walking out and a smug Higgins believing that she will return. Whether she does or not is immaterial. The fact that she has a choice of many different lifestyles -live with Higgins as an "old bachelor," marry Higgins, marry lovelorn Freddy Eynsford-Hill, marry someone worthy of her, not marry at all- is where the trajectory of her life is leading. Choice is her triumph.
That makes sense.
To end showing her ultimate decision -whatever that might be- is to rob audience members of finishing the story for themselves.
The choice they end with in the 1964 version is particularly grim. Harrison plays Higgins with a relentless, brutal bite.  Which works since the original Higgins is meant to be incorrigible and manipulative.
However, this means that Eliza must match him in strength of will or else be a victim. Audrey Hepburn plays it strong throughout. She is a match for Harrison. However, that last scene seems to cancel everything. Hepburn gazes tenderly at Harrison as she returns to his realm and he says "Where the devil are my slippers?" This could be a simple playful reference to an earlier conversation, or he actually expects her to come back as his quasi-servant.
Because there isn't the slightest bit of tenderness that Eliza says she wants from Higgins [though one could argue there is affection for her in secret when Higgins is alone singing "I've Grown Accustomed to Her Face."], her return at the end is odd.
 Higgins and Eliza complement each other well. His world represents theory that never really gets a practical application until Eliza shows up. Eliza represents raw reality. Her need for the science of speech is for pure survival. When he goes overboard and makes a grand lady of her who is too high-bred for both the slums and the middle class, Eliza feels she's overshot her goal of working in a middle class flower shop. Higgins has no sense of practicality. This brings the ultimate tension where they consider parting ways.
 The 1938 film version of My Fair Lady's predecessor, Pygmalion, with Leslie Howard and Wendy Hiller also sees Eliza return. However, Howard plays Higgins with occasional bouts of tenderness toward Eliza.[Robert Powell would later do the same in his performance for the BBC in the 1970s.] Hiller plays the character tough enough to make it clear that Eliza is returning, not to be abused, but to be an equal, one of the "old bachelors." The 1964 version fails to leave Eliza strong, making her return unpalatable.
- Shmuel Ross goes into greater detail on the ending of the story in the article Visions and Revisions of the End of Pygmalion. I didn't realize this is an old debate until I began researching Shaw's original intent. Apparently, since the beginning, everyone has wanted to change the last scene to a more traditional comic ending where hero and heroine end up together, even though there is no reason to believe they would want to or should.
- The newer movie promised a more Shavian bent. However, Emma Thompson, the screenwriter, is thoroughly dismissive of the 1964 film. One wonders if the film she planned would have been recognizable. You may read Thompson's comments on the My Fair Lady remake at Variety: Thompson Has Plenty on Filmaking Fire.