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The word an in this sentence (indefinite article) means that the word animal is non specific. So this structure does not follow from the original. "A is B" is not the same as "A is a B"

However, you are right that it's not always correct since "Poetry is Literature" and "Steam/Ice is H20" are both examples where this breaks down.

My annoying pedantry for the day.

you can do the same mistake without “an”.

Jeff is the short haired guy != the short haired guy is Jeff.

It depends on context. You can’t fully equate them.

"A is B" is meant a bit loosely here. A better shorthand would be "A is the B" <=> "The B is A", or "A does B" <=> "B is done by A".

The actual paper explores equivalences that actually make sense, and whether LLMs have trouble with them.

This is bad news for all the people who like to say "A winner is you!"

But obviously that implies that you are a chicken dinner.

At least according to some people's expectations, presumably.