of each other was close because they were both poets: reading these letters, one senses that Eliot finds it hard to let himself be open with anyone who doesn't have the skill to do what he does. With a fellow poet, he can discuss what is really important to him in language he knows will be understood.
Also, while he was socially adept and keen to become more so, Eliot's intimate world remains exceptionally small.
from Telegraph: T.S. Eliot does not correspond with his letters