“Oh, you can’t help that,” said the Cat: “We’re all mad here. I’m mad. You’re mad.”
“How do you know I’m mad?” said Alice.
“You must be,” said the Cat, “or you wouldn’t have come here.”1
“No one’s really sure if the Cheshire Cat is a friend or not. Alice thinks of the Cheshire Cat as a friend and wants to talk with him, but it turns out that she can’t communicate with him and has no idea how he disappears and reappears so suddenly. The Cheshire Cat makes jokes and disappears when she needs him the most.
The Cheshire cat is most easily distinguished by its unusual ability to remove its head from its body when it wants to disappear from view and reappear somewhere else. When Alice first encounters the Cheshire cat, it leaves its body behind and taunts her about never being able to reach him. He later torments her by speaking to her head-first (and leaving his body behind)
In their third meeting, at the croquet game, just the grin of the cat appeared first, then…“Alice waited till the eyes appeared, and then nodded. ‘It’s no use speaking to it,’ she thought, ‘till its ears have come, or at least one of them.’ In another minute the whole head appeared, and then Alice put down her flamingo, and began an account of the game, feeling very glad she had someone to listen to her. The Cat seemed to think that there was enough of it now in sight, and no more of it appeared. “
The Wonderland is an allegory for consciousness. The Cheshire Cat represents the subconscious, and the true nature of reality- the grinning paradox- the reality that there is no high or low. They are antithetical to the Queen, which represents repressive control. The Cheshire Cat won’t kiss the kings hand (refusing to admit his dominance) and then is to be beheaded. But the executioner can’t behead the Cat as their body disappears. Then their head disappears, illustrating that even the most repressive tactics cannot suppress the absurd, paradoxical, whimsical nature of the wonderland… the reality of the mind itself.”2
1 https://www.booksie.com/665032-down-the-rabbit-hole
2 https://lymmradio.co.uk/2022/02/17/the-cheshire-cat-11-weird-things-people-believe-some-are-true/