not_protected.rb

class A 
  def hello 
    "A#hello"
  end

  def method_missing(method, *args)
    "A#method_missing"
  end

  protected :hello
end

p A.new.hello # => "A#method_missing"

Crap, stuffed that up. Ok, try this on for size:

class A
  def hello
    "A#hello"
  end

  def method_missing(method, *args)
    "A#method_missing"
  end
end

class B < A
  def hello
    "B#hello"
  end

  def goodbye
    "B#goodbye"
  end

  protected :hello, :goodbye
end

p B.new.hello   # => "A#method_missing"
p B.new.goodbye # => "A#method_missing"

And also

A.new.hello
=> "A#hello"

Right, so you can hide functionality in a subclass that is provided by the superclass.
That sounds like a bad idea, since it sort of stops you being able to rely on object-oriented polymorphism.