How does Eliza undermine Higgins' image of himself and make him uncomfortable?

Eliza asks whether her clothes belong to her or Pickering, since he is the one who bought them. Higgins replies that of course they belong to her. When she protests that she did not want to be accused of stealing them, he is hurt. (She has not forgotten her roots in poverty.) He says that that her comment shows a want of feeling. Eliza pushes her advantage, asking him to take the hired jewels to his room so that they will be safe. Higgins exclaims that he would shove them down her throat if only he would not have to return them to the jeweler. Eliza also gives Higgins back a ring that he bought her, a piece of jewerly that was not borrowed. He angrily throws it into the fireplace and says that she has "wounded him to the heart."