I can imagine when you want some attribute to be only readable, or be writable and readable, but not when you want an attribute to be writable and not readable.
In some cases, you might want to read some attributes but not be able to change them. For example, if you have an Animal class and want to initialize it with a name, age, and color, you could write
attr_accessor :age, :color
and then for name have
attr_reader :name
because a name doesn't change. A cat can get older or change color, but the name (for the sake of this question) once assigned should not be changed.
On the other hand, I cannot rationalize a scenario (aside form passwords) where you would need attr_writer (as opposed to attr_accessor or attr_reader). Under what circumstances would you want to write something, but not want to read it? What type of scenario or situation calls for attr_writer?
If you can think of a scenario in other programming languages, that is welcome but my immediate scope of Object Orientation knowledge is within Ruby.