What's ironic in "Everything that Rises Must Converge" by Flannery O'Connor?

One of the most important ironies in the story is that Mrs. Chestny's very expensive and unique hat is also worn by an African-American woman on the bus.  Mrs. Chestny proudly says multiple times that she "wouldn't meet [herself] coming and going" while wearing this hat, and there are a few reasons for this: first, it is quite distinct, and, second (and more importantly), it is expensive.  Mrs. Chestny is proud of her ability to purchase such a costly hat, and she believes that her financial position makes her somewhat unique among her neighbors.  She is also white and a racist.  Thus, when she sees another woman and, even more upsetting to her, a black woman, wearing that same hat, it signals to her that the world is no longer the place she's known her whole life and that her position in that world is not what it used to be (two ideas that her son, Julian, has been trying to impart to her throughout the text). 

Mrs. Chestny then tries to give the black woman's son a penny, as if to try to reinstate this old world and position herself above the other woman, but her action backfires when the other woman strikes her.  The irony of this other woman, a woman Mrs. Chestny perceives as being beneath her in both racial and socioeconomic status, wearing the same hat as Mrs. Chestny really symbolizes the title of the story: as the races begin to become more equal, legally and financially, it is inevitable that they will converge, and this convergence will create problems for those who are unwilling to accept this new, more equal, world.