In George Bernard Shaw's play Pygmalion the character of Eliza seems to have developed a connection with Higgins. This connection occurs as a result of him having rescued and refined her from the streets where she first worked as an uneducated flower girl. The fact that he takes the time to reform her seems to Eliza a symbol of care that she much needs. However, she is quick to realize that Higgins is not a romantic man and that his goal of educating Eliza is nothing but his own ambitious way to proof a point: That he is a good enough linguist to turn a flower-girl into a duchess.
However, we see that, at the end of the play in Act V, Eliza's tough surface begins to break while she explains to Higgins what her needs are as a person. It is highly improbable that she would have even brought up the topic had she not wanted some reaction from Higgins to that respect.
[much troubled] I want a little kindness. I know I'm a common ignorant girl, and you a book-learned gentleman; but I'm not dirt under your feet. What I done [correcting herself] what I did was not for the dresses and the taxis: I did it because we were pleasant together and I come—came—to care for you; not to want you to make love to me, and not forgetting the difference between us, but more friendly like.
The reaction that she gets from Higgins at his point is so negative, brash, and awful that she goes back to a defense mode clarifies what a brute she thinks Higgins is (because he is a brute, indeed) and she goes on and on as to who she wants in her life for sure.
However, the story itself narrates how the relationship between Eliza and Higgins has a unique connection, and that perhaps this is the way that they are meant to live in the first place: Close but not together.
To put it shortly, she knew that for some mysterious reason he had not the makings of a married man in him, according to her conception of a husband as one to whom she would be his nearest and fondest and warmest interest
This tells us that there is indeed a certain feeling inside of Eliza which, by nature, makes her suppose that she is meant to be married to Higgins for the fact that he is a bachelor, they shared a huge experience together, and she is of a marriageable age.
But then we encounter what ultimately decides for Eliza: She is just as strong, just as tough,and just as dominant as Higgins. Their relationship certainly would not be too successful, from what we can tell.
Put that along with her resentment of Higgins's domineering superiority, and her mistrust of his coaxing cleverness in getting round her and evading her wrath when he had gone too far with his impetuous bullying, and you will see that Eliza's instinct had good grounds for warning her not to marry her Pygmalion.