I see the top implementation of class level private methods a lot. Please understand that the private means nothing in that case. Do you know why? :)

class_level_privates.rb

# The wrong way to make a class level method private

class Foo
  def self.bar
    p "bar"
  end
  
  private
  
  def self.baz
    p "baz"
  end
end

Foo.bar   # => "bar"
Foo.baz   # => "baz"

# The right way to make a class level method private
class Cat
  class << self
    def hat
      p "hat"
    end
    private
    
    def hidden
    end
  end
end

Cat.hat # => "hat"
Cat.hidden # => private method `hidden' called for Cat:Class (NoMethodError)

For making class methods private, you can also use private_class_method.

As for why the private keyword does nothing for self.foo style method declarations, I've come to understand it this way (after some late night reading!):

You cannot make methods private when they are given an explicit receiver (as in self.baz). Therefore, to make class methods private, you have to open up the "eigenclass" of the class. In that context, the class (Cat or Foo is the implicit receiver (it's an instance of the eigenclass), and so doing

class Cat
  class << self
    ...
  end
end

Makes the Cat class itself (and not an instance of the Cat class) the implicit receiver. Now you can declare private class methods.

Maybe none of that matters anyway because I can just do Cat.send(:hidden) and break the visibility rules!