The tense relationship between Eliza Doolittle and Henry Higgins is the basis of Pygmalion's central conflict. Initially, this does not appear to be so: Higgins makes a bet that he can pass Eliza off as a duchess by teaching her upper-class English, and so the two have to work together to achieve this goal. However, once Higgins wins his bet, he does not acknowledge Eliza's role in the success and does not seem to consider how his games affect her.
Eliza comes to resent Higgins's treatment of her. She feels her hard work deserves to be acknowledged. She also feels Higgins is callous in not considering how her social role has been changed by the bet: she now no longer fits wholly into the lower or upper classes. Higgins is offended by Eliza's hurt reaction, calling her a "heartless guttersnipe" when she returns the ring he'd given her. He seems unable or unwilling to consider her reaction as anything other than histrionics.
The conflict resolves when Eliza chooses to leave Higgins. She decides she will marry Freddy and perhaps even teach others how to speak the way that Higgins has taught her. She has become fully independent. Ironically, Higgins likes Eliza's newfound fire and credits himself for its existence, but the ending scene strongly implies she has no interest in returning to him.