kind of way.  She wants to hurt Mrs. Ansley. Mrs. Slade is unhappy with her life.   

Mrs. Slade thinks that she is in control of the situation, having written the letter to her friend, she thinks that she fooled her into waiting, and waiting for the man she was engaged to.  Now Mrs. Slade is bitter and looking to put Mrs. Ansley in her place once and for all.

But it is Mrs. Ansley who has the most surprising news to tell.  She is the more sympathetic character of the two.  I think that the author favors her, Mrs. Slade wants to hurt Mrs. Ansley.

Then Mrs. Ansley tells Mrs. Slade the truth about her tyrst with Delphin,

"Mrs. Ansley had not moved for a long time. But now she turned slowly toward her companion. "But I didn't wait. He'd arranged everything. He was there. We were let in at once," she said." (Wharton)

Mrs. Slade still feels smug, she says,

"At the end of all these years. After all, I had everything; I had him for twenty-five years. And you had nothing but that one letter that he didn't write." (Wharton)

Then Mrs. Ansley says, I had Barbara.  

Judging by the manner in which Edith Wharton characterizes Mrs. Slade and Mrs. Ansley, it is safe to say that it is not too difficult for a female reader to identify with either of the two. For once, the ladies were wives (now widows) and mothers. As typical females, they experience bouts of likes and dislikes regarding each other's lives, successes, or failures. Additionally, their similarities may render them prone to compete with each other. It is all the nature of human behavior. Yet, it is in the way that Mrs. Slade is presented as abrasive and somewhat haughty, that the reader is led to connect more with Mrs. Ansley 

There is also evidence of Wharton's own partiality toward Mrs. Ansley. After all, it is she who Wharton selects to be the character that gives the presumptious Mrs. Slade the final "knockout". This happens when Mrs. Ansley reveals that her daughter Barbara was actually conceived with the late Mr. Slade even after Mrs. Slate's desperate attempts to keep the two separated during their engagements. In her attempt, Mrs. Slade writes a fake letter where her then-fiancé, Delphin, presumably wanted a meeting with Grace (Ansley) only to make Grace go and get jilted.

The outrageous confession of Mrs. Slate is what breaks the sympathy with the reader, for it is clear that her decision could have hindered Mrs. Ansley's life in many ways. The fact that the fate is different, and Mrs. Ansley did get to be with her beloved Delphin, makes the story's twist all the more satisfying to the reader.