Self-schizophrenia example

gistfile1.rb

# Self-schizophrenia example

class A
  def foo
    "foo"
  end

  def bar
    "bar"
  end

  # Crucially, the invariant should be that this method returns 
  # whatever foo returns, plus whatever bar returns
  def foobar
    foo + bar
  end
end

# Now with delegation:

require 'delegate'
class B < DelegateClass(A)
  def foo
    "baz"
  end
end

b = B.new(A.new)
b.foo # => "baz", all is fine
b.bar # => "bar", all is fine
b.foobar # => "foobar", arrrgh, inconsistency: should be "bazbar"

# But with mixins, DCI-style:
module C
  def foo
    "baz"
  end
end

a = A.new
a.extend C
a.foo # => "baz", all is fine
a.bar # => "bar", all is fine
a.foobar # => "bazbar", all is fine

I think you are doing it wrong in a DCI context.
In DCI, you'll want to decorate your object to add behaviours, not to overwrite them, so having a foo method in A class doesn't makes sens.