This duckling made me think of this dog from reddit, that I made into a telegram sticker a while ago:

He’s in bean jail for bean crimes

Is this your dog?

Cowa Cola

It’s easy to understand, when you turn the brackets into readable characters.
o for opening bracket (
c for closing bracket )

So ()() would be ococ, which is coco backwards and clearly not a palindrome.

())( would be occo, which is a palindrome.