A purrfect match.

Which famous feline are you?

You're the Cheshire Cat. Your mysterious aura and your penchant for riddles keep your friends guessing. You dislike staying too long in any one place. Your advice is always sound, if somewhat enigmatic. The sum total of this is that people are always following you and you just WANT TO GET AWAY!
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I always wanted to be the Cheshire Cat. He could disappear everything but the grin, an admirable quality. I value my grin, (it's what I have instead of a smile), and when it disappears and I remain, it's a very bad omen for me, a dark time. People ask my advice, but I shake my head. I have no desire or inclination to screw up your life. You will have to do that on your own. I do always want to get away... here I go... *poof*

Cheshire cat dialogue:

"But I don't want to go among mad people," Alice remarked.
"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."
Alice didn't think that proved it at all: however she went on. "And how do you know that you're mad?"
"To begin with," said the Cat, "a dog's not mad. You grant that?"
"I suppose so," said Alice
"Well, then, " the Cat went on, "you see a dog growls when it's angry, and wags its tail when it's pleased. Now I growl when I'm pleased, and wag my tail when I'm angry. Therefore I'm mad."
"... thought Alice, and she went on. "Would you tell me, please, which way I ought to go from here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where –" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"– so long as I get somewhere," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long enough."

Found via Silly Humans.