Analysis of "Eleanor Rigby"

The theme of this song is certainly not subtle: it's about lonely people. But stating it thus doesn't do justice to what the Beatles were really saying. A closer inspection reveals that this song examines why the lonely people are lonely.
The song has two characters, Eleanor Rigby and Father McKenzie. These two are connected by the church, in this case the actual church that Father McKenzie preaches at and Eleanor Rigby cleans. She is -- and this is not apparent immediately -- a custodian in this church. How do we know that she's the custodian? Well, she picks up rice after weddings.…