Problem that I don't understand with Rails relations

category.rb

# $ rails new foo
# $ cd foo
# $ rails generate model Category position:integer parent_id:integer name:string children_count:integer
# $ rake db:migrate

# Modified app/models/category.rb
class Category < ActiveRecord::Base
 
  attr_accessible :position, :parent_id, :name
 
  has_many :children, class_name: "Category", foreign_key: :parent_id, inverse_of: :parent
  belongs_to :parent, class_name: "Category", counter_cache: :children_count, inverse_of: :children
 
  default_scope order('position ASC')
 
  def last_child
    children.last
  end
end

# Rails console

c1 = Category.create(name: "Category 1")
Category.create(name: "Category 1.1", parent_id: c1.id)
Category.create(name: "Category 1.2", parent_id: c1.id)
c2 = Category.create(name: "Category 2")
Category.create(name: "Category 2.1", c2.id)

c = Category.first
c.last_child # Makes a DB request
c.last_child # Makes a DB request
c.last_child # Makes a DB request
 
c.children # Makes a DB request
c.children # No longer makes a DB request
 
c.last_child # No longer makes a DB request
c.last_child # No longer makes a DB request
c.last_child # No longer makes a DB request

 
# Tried changing this in the model, but the problem is the same
# When calling last child without calling children alone before
# there is no use of the cached query
def last_child
    children && children.last
end