çıkıyorum - I am going.
I understand your English answer clearly & it is correct to me. Duo does not have "exiting" in its data bank of answers & does not recognise the word to identify it as a correct answer.
Exiting - çıkarken.
çıkarken - On the way out. (or) Whilst I left.
"Hastaneden çıktım" - I have left the hospital.