There are two central quotes that any analysis of the theme of loneliness in this brilliant short story must identify and comment upon. What is interesting about these two quotes is the way in which they are actually related, as the first quote is used by Miss Brill to describe the lonely lives of others, whereas the second uses the same words to describe her own lonely life at the sad ending of this tale.
Note the way that Miss Brill describes the people that sit around her who she notices come every weekend without failure to sit on the benches:
They were odd, silent, nearly all old, and from the way they stared they looked as though they'd just come from dark little rooms or even--even cupboards!
The way in which Miss Brill refuses to identify herself with the "strange" people amongst which she sits shows how she is unable to see the truth of her condition. Her description of the loneliness of others is strengthened by imagining that they emerge from "cupboards" to come out and sit down. However, note the way that at the end of the story, after overhearing the cruel words of the young couple, she comes to apply the same description to her own life:
But today she passed the baker's by, climbed the stairs, went into the little dark room--her room like a cupboard--and sat down on the red eiderdown.
This quote shows that at least at some level she recognises that she is just like those other people who lead lives consumed by loneliness. In spite of all of her elaborate fantasies, she is forced to recognise the way in which she has an empty life and is incredibly lonely.