Portrait of a Lady Isabel Archer doesn't go away with Casper Goodwood because it would mean giving up what she values most, her freedom and independence. The very first time we meet Isabel she tells Ralph that "I'm very fond of my liberty" (p. 30) and that she is "not a candidate for adoption" (p. 29). Both of these statements clearly show early on that she is not looking to be tied down at all. She wants to be free to experience all that life has to offer for her. Because of that, she turns down the proposal of Lord Warburton, although he had much to offer. James says, "The idea of a diminished liberty was particularly disagreeable to her at present, since she had just given a sort of personal accent to her independence by looking so straight at Lord Warburton's big bribe and yet turning away from it" (p.
104). She goes on to show her independence when she speaking with Casper Goodwood by saying, "it's no kindness to a woman to press her so hard, to urge her against her will" (p. 137). Isabel came to Europe because she wanted to experience life and the freedom that eluded her in America.
At the beginning of the novel, Isabel was very young morally. She had left everything she had known, and was ready to start anew. Throughout the novel, her morality grew, changed, and became more stable. Where at the beginning she refused two proposals of marriage, without giving any indication to wanting a third, she ends up accepting a proposal from Osmond. Goodwood's offer to Isabel came at an early stage of her moral growth, when she was not really sure of what she wanted, so she could accept. She was beginning to enjoy her newfound freedom. After her refusal to Goodwood, Isabel's throbbing heart was due to two reasons, her discussion with Goodwood and "simply the enjoyment she found in the exercise of her power" (p. 143). Her power was her newfound freedom, her ability to judge however she liked and make her own decisions, no matter the consequences. Isabel said "to judge wrong, I think, is more honorable than not to judge at all (p. 140). She wanted the freedom to judge, and to act on those judgments. By marrying Goodwood, she would be giving up some of that freedom.
Another reason to refuse Goodwood's offer was because accepting his proposal of marriage would mean returning to America. To Isabel, America was not a very fulfilling place. Her father had just died, and she was living in a house by herself. There was very little room for her to grow or become the independent woman that she wanted to be. When Mrs. Touchett showed up at her door to take her away, she looked at it as her big chance to experience the life that she could not find in America. At her arrival in Europe, she was immediately experiencing new people and places. She was in a totally different world, where the people valued life, art, and were more civilized. She had finally found a place where she could grow both emotionally and morally. Goodwood's proposal would have taken her away, back to America, where in Isabel's mind there was no more room to grow.