How is the main character of "Miss Brill" an outcast?

In Katherine Mansfield's short story "Miss Brill", the eponymous main character is certainly a social outcast in several ways. 

While this may sound like a harsh descriptor, in reality, Miss Brill was one who seemed to prefer to carry on with life on her own. We know very little about her past to determine what could have triggered this choice of lifestyle. What we do know, however, is that she seems to be so used to a lonely life that she has taken to give identities and create life stories for those whom she sees walking casually around the park. 

• Self-absorbed

Again, this is another seemingly harsh and critical descriptor, but it fits Miss Brill quite perfectly, according to its definition. Miss Brill does very little to change her lonely status. She does not try and find ways to meet people. Instead, she is consumed with her lifestyle and gives little space to any new events. This isolation from society, and the insistence in keeping life going her way in her own particular approaches, are the factors that make Miss Brill into a bona fide outcast.

• Out of sync

Living in isolation for such a long period of time makes it very hard for anyone to keep up with the real dynamics, issues, and changing trends that take place in society every day. The fact that these factors change dramatically from one moment to the next, makes it even more important to keep up with life as much as possible. Miss Brill has not even changed the fur that she has worn for decades, let alone her attitude toward things. She will realize exactly how out of synch she is when she hears the lovers in the park laughing about her. 

"No, not now," said the girl. "Not here, I can't." "But why? Because of that stupid old thing at the end there?" [...] "Why does she come here at all–who wants her? Why doesn't she keep her silly old mug at home?"  

"It's her fu-ur which is so funny," giggled the girl. "It's exactly like a fried whiting." "Ah, be off with you!" said the boy in an angry whisper.

While the story lacks a specific, direct characterization that critically assesses the appearance of the old teacher compared to the rest of the world, the reactions of this couple definitely tell us that Miss Brill must be definitely not just an outcast in spirit, but also in her overall appearance.