From the passage we know:
Beautiful cats --subset-> Persian --all--> pompous --all--> irritating.
So we need to find an answer that does not directly fit into this chart.
A) This has to be true, because working backwards from the chart, all persians are irritating and some of the beautiful cats are persian
B) Also must be true for similar reasons working backwards in the chart
C) Trick answer, but this is actually TRUE. We see that under Persian, it always points down to irritating. Don't eliminate an answer just because it uses words like "all".
D) Must be true, just like irritating, work backwards from pompous cats, which are all Persian cats.
E) Not always true, we know nothing about non-Persian cats, for all we know they could all be NOT irritating, or they could ALL be irritating, in either case the chart above still holds true.
Choice
E is correct.