The question is asking for us to determine the one answer choice that doesn't have to be true.
Let's look at the final chain produced by the premises in the passage.
World's most beautiful cats -some- Persian Cats -> Pompous Cat -> Invariably Irritating Cat
Answer choice C states:
NOT invariably irritating -> NOT Persian cat
This is the contrapositive of a portion of our chain. That is how we know it must be true.
As for answer choice E, we don't know anything about a group of irritating AND beautiful cats. Invariably irritating is not sufficient for any condition. Nor is being a beautiful cat. Only the world's most beautiful cats are a sufficient condition.
I hope this helps. Please let me know if you have any other questions.