I have the feeling you haven't read the story. There are only three female characters, and two of them appear at the very end and play a very small part in the story.
Phoenix is the main character, an elderly African American woman who walks to town to get medicine for her grandson. No matter what gets in her way, be it a thorn bush or a dog or falling into a ditch, she is determined to get the medicine. The eNotes character analysis says: "Phoenix's name is symbolic of the mythological bird who rises from its own ashes to begin another cycle of life. The old woman's name thus suggests her timelessness and the fact that she can never be suppressed, even by those who would try to break her spirit."
Now, read the story, and you'll see why she is such a strong person. You would know when she came into a room, and you'd probably enjoy talking to her!