It is worth remembering the end of the Just So Story of the Cat That Walked By Himself:
Then the Woman laughed and set the Cat a bowl of the warm white milk and said, ‘O Cat, you are as clever as a man, but remember that your bargain was not made with the Man or the Dog, and I do not know what they will do when they come home.’
‘What is that to me?’ said the Cat. ‘If I have my place in the Cave by the fire and my warm white milk three times a day I do not care what the Man or the Dog can do.’
That evening when the Man and the Dog came into the Cave, the Woman told them all the story of the bargain while the Cat sat by the fire and smiled. Then the Man said, ‘Yes, but he has not made a bargain with me or with all proper Men after me.’ Then he took off his two leather boots and he took up his little stone axe (that makes three) and he fetched a piece of wood and a hatchet (that is five altogether), and he set them out in a row and he said, ‘Now we will make our bargain. If you do not catch mice when you are in the Cave for always and always and always, I will throw these five things at you whenever I see you, and so shall all proper Men do after me.’
‘Ah,’ said the Woman, listening, ‘this is a very clever Cat, but he is not so clever as my Man.’
The Cat counted the five things (and they looked very knobby) and he said, ‘I will catch mice when I am in the Cave for always and always and always; but still I am the Cat who walks by himself, and all places are alike to me.’
‘Not when I am near,’ said the Man. ‘If you had not said that last I would have put all these things away for always and always and always; but I am now going to throw my two boots and my little stone axe (that makes three) at you whenever I meet you. And so shall all proper Men do after me!’
Then the Dog said, ‘Wait a minute. He has not made a bargain with me or with all proper Dogs after me.’ And he showed his teeth and said, ‘If you are not kind to the Baby while I am in the Cave for always and always and always, I will hunt you till I catch you, and when I catch you I will bite you. And so shall all proper Dogs do after me.’
‘Ah,’ said the Woman, listening, ‘this is a very clever Cat, but he is not so clever as the Dog.’
Cat counted the Dog’s teeth (and they looked very pointed) and he said, ‘I will be kind to the Baby while I am in the Cave, as long as he does not pull my tail too hard, for always and always and always. But still I am the Cat that walks by himself, and all places are alike to me.’
‘Not when I am near,’ said the Dog. ‘If you had not said that last I would have shut my mouth for always and always and always; but now I am going to hunt you up a tree whenever I meet you. And so shall all proper Dogs do after me.’
Then the Man threw his two boots and his little stone axe (that makes three) at the Cat, and the Cat ran out of the Cave and the Dog chased him up a tree; and from that day to this, Best Beloved, three proper Men out of five will always throw things at a Cat whenever they meet him, and all proper Dogs will chase him up a tree. But the Cat keeps his side of the bargain too. He will kill mice and he will be kind to Babies when he is in the house, just as long as they do not pull his tail too hard. But when he has done that, and between times, and when the moon gets up and night comes, he is the Cat that walks by himself, and all places are alike to him. Then he goes out to the Wet Wild Woods or up the Wet Wild Trees or on the Wet Wild Roofs, waving his wild tail and walking by his wild lone.