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The entire song is made up of palindromes. It contains the following variation of the post title:

Was it a car or a cat I saw?

The fact that it's a parody of a Bob Dylan song and Bob is itself a palindrome, is the cherry on the cake. It's my favourite Weird Al song for this reason.

And it was released in 2002.

20 February, by any chance?

This article has broken my brain. I read this and stared at it like "this isn't a palindrome? What are you on about?"

Its funny how this is also a palindrome.

I'm sure it was unintentional.

aibohphobia being both a palindrome and the word for fear of palindromes is absolutely intentional.

I'm sure you understand sarcasm.

no, what's that

Then what will we call the fear of that little robot dog that Sony made?