Hi guys & gals,
<- New user.
I've read both jazzy and Salmoe's posts about the Eliza and Higgins' relationship being entirely a platonic one; based partly on the line where Eliza says she'd like to be friendly-like with Higgins.
I'm of opposing interpretation.
I mean, I've only watched the movie a few times but I give you this evidence:
Now, I'm not arguing the relationship became platonic after the ball when he offended her by taking all the credit for himself, and before she comes back to him.. But, obviously she has juvenile feelings for him before the ball. But, his feelings for her take a bit more evolving. First, simply having her around, then more fully when she gains a bit more independence.
First off, he patronizes her constantly. This is quite common amongst student teacher relationships, but also amongst regular relationships. By constantly patronizing her he paints her a picture where she is ever struggling to prove herself to him. This gives both him and her meaning.
For this viewer it appears that Eliza has been wounded so badly when her expectations where shattered after the ball that her ego forces her past a few of insecurities after visiting Higgins's mother; thus attracting Higgins further.
Although he is in conflict about how he should feel toward Eliza, he steadfastly stays the course and goes home. Higgins understands he must maintain his leadership despite her newfound independence for their relationship to be successful ("now where are my slippers /credits).
Furthermore, this part of Higgins's is awesome:
This quote is very relevant when it comes to relationships. One of the major points in a relationship is not whether you treat someone badly, but whether you treat them better than everyone else around you.
You can see Higgins is the experienced bachelor while Eliza is a completely inexperienced. "I'm a good girl, I am!" The point is by the end of the play she is still inexperienced in relationships. This never changes despite her gaining some confidence amongst higher classes.
This idea about them becoming equals still exists to some extent:
This displays that she simply wants acknowledgment. My point is if you asked her the night of the ball she would have sung a different tune. The only problem was that Higgins hadn't realized he was attracted to her at that point, and it was his God-given right to enjoy success with one of his boys, Colonel Pickering.
It's similar to the situation where you unexpectedly break up with a girl and one of the first things out of her mouth is how she was planning to break it off later that night.

Typical reaction.
Riiiiiight. Yet you ended up getting giddy about dancing with Higgins!
This is the first time Eliza has been attracted to a guy like Higgins and circumstances didn't work out so of course she'll say she doesn't want to make love to him or think of him as a love interest. Yet, at the end, she comes back, Higgins immediately patronizes her, and she enjoys it.
Higgins is the classic successful bachelor! Because of her new-found independence he is more attracted to her. And, in the end she realizes she could never settle down with someone so boringly nice like Freddy or Pickering so she goes back to Higgins.
Personally, I think the only person who has experience in relationships that could deny feelings between the two characters is doing the story an injustice. Maybe they don't want to encourage the actors to play the Student/ Teacher romantic interest because it is taboo? Maybe they've read all of the older revisions for so long they can't accept an audience's expectantly uneducated interpretation?
Higgins is brimming with confidence and experience. What girl wouldn't be attracted to that?
Regardless, I think we can all agree that this piece of work manages to satisfy a whole slew of personality-types by having such interpretive and contradictory scenes.