Why would the part "nem ez szék" be considered wrong? Does the inclusion of "Ez" at the beginning automatically make all other objects out to be "a" instead of "the", unless specified otherwise?
"ez NEM egy asztal, hanem egy szék" would be a gramatically correct sentence, but that would rather be "this is not a table, but a chair".
"ez egy asztal, nem egy szék" should be fine though for this lesson.