In the sentences:
1)Ist das die Professorin?
-Nein, das ist nicht die Professorin.
Here 'nicht' precedes the definite article 'die'. This is because the noun 'Professorin' is preceded by 'die'
2)Siehst du den Stuhl?
-Ich sehe den Stuhl nicht.
Here 'nicht' is placed at the end of the sentence because 'Stuhl' is the object in the sentence.
[Ref:https://resources.german.lsa.umich.edu/grammatik/nicht/ https://deutsch.lingolia.com/en/grammar/sentence-structure/negation https://www.thoughtco.com/the-position-of-nicht-1444481]
In sentence_1 why can't we place nicht at the end of the sentence as 'Professorin' is the object in the sentence .i.e. why is 'Nein, das ist die Profesorin nicht' wrong?
In sentence_2 why can't we place 'nicht' before 'die Stuhl' as the noun 'Stuhl' is preceded by definite article 'die' .i.e. why is 'Ich sehe nicht den Stuhl' wrong?
Thank you for your time and thoughs.