~기는(요) =  Used to emphatically disagree with a previous statement

(shows modesty in reaction to a compliment) x

이 책을 다 읽었어요? = Have you finished reading the book?
끝나기는요? 책을 읽는 것을 시작하지 않았어요! = Finished? I haven’t started reading it!

지금 너무 춥죠? = It’s really cold now, right?
춥기는요. 다음 달에 기온이 더 낮아질 거예요. = Cold?! Next month the temperature will get lower.

한국말을 잘하시네요. = You speak Korean really well.
잘하기는요. 아직도 실수를 많이 해요. = Well? I still make lots of mistakes.

옷을 잘 입어요. = You dress very well.
잘 입기는요. = Dress well? Oh not at all… (blushing)

~기는(요) is sometimes simply the ~기 nominalizer followed by topic particle 는 i.e. speaking of… when it comes to… as for...

칠칠맞기는 = Talk about sloppy.
살아 있기는 살아 있을까? = But do you suppose they’re really alive?