In Pygmalion, we see different types of influence and control, sometimes literal and other times metaphorical: the teacher training his student, the artist shaping his creation, the con artist fleecing his mark, the child playing with his toy. That said, these roles aren't always well-defined; they can change easily, without warning. Sometimes the master becomes the slave and the slave the master, in the blink of the eye, while other times the two simply become equals. Shaw wants us to observe the consequences of control, to see how these changes occur.
Shaw asserts that manipulation and coercion are presented as natural, necessary modes of action. Without them, real change – personal and societal – would not be possible.
In recognizing Eliza as his equal at play's end, Higgins is really recognizing the extent to which he has manipulated his subject. Eliza has changed, yes, but Higgins's perceptions have changed even more.