How is "Pygmalion" a tragedy of knowledge?
Who says that? 'Pygmalion' is not at all a tragedy but rather a comedy of manners.
However, there is an ironic twist of fate which leads to Liza's 'downfall' in several ways. Liza betrays her identity by speaking English too well, thus making Higgins lose his bet. But the transformation is only superficial - she becomes an educated flower girl without truly being erudite. In Act III Liza's coarse conversation shocks Mrs Higgins and Mrs Hill but she is oblivious to her social offense:
"Have I said anything I oughtn't?"
Moreover, now that she is educated, Liza no longer belongs to the lower class, either. In Act IV, she laments to Higgins:
"What am I fit for? What have you left me for? Where am I to go? What am I to do? What's to become of me?
I sold flowers. I didn't sell myself. Now you've made a lady of me I'm not fit to sell anything else. I whish you'd left me where you found me."
In the play's final scene, it is a small comfort to see Liza's defiance in submission to Higgins' whims. Concerning the clothes order Higgins places, she retorts, "Buy them yourself," but Higgin's dismissive remark to his mother is the final word:
"Oh, don't bother. She'll buy 'em all right enough. Goodbye."
As the curtain draws, the audience realizes that in the battle of the sexes (the most important 'bet,' after all), Higgins at least thinks he has "won."