Since 'cette fille' is referring to a specified girl, as explained in case 2b, shouldn't we use 'elle est'?
This question seems to have been asked a lot recently, so perhaps the lesson is not clear enough.
Case 1 is "c'est" + noun / name. You must always use "c'est" here.
Case 2 is "c'est" or "il/elle est" + adjective. This depends on whether it's specific or non-specific.
So your example is covered by case 1 and you have to use "c'est". I disagree with Chris here, I don't think "Elle est Marie" is correct.
You might find this link useful:
C'est Marie. -- It is Marie.Elle est Marie. -- She is Marie.
Qui est cette fille? C'est Marie. -- Who is that girl? It's Marie.
I don't know how to motivate it any better. Sometimes you just have to take things the way they are. Language isn't math and many rules are, at best, guidelines.
In particular in French I sometimes feel that rules are only there to justify the countless exceptions. ;)
-- Chris (not a native speaker).
I think it would be worth adding to the lesson an explicit statement that phrases like "il est mon frère" are wrong. (Not everyone will read the Q&A.)
"Il est mon frère" is so natural for an English speaker that it really has to be emphasised that it is incorrect, otherwise we just assume that both "c'est mon frère" and "il est mon frère" are correct, and then we probably make the further error that one means "it's my brother" and the other means "he's my brother".
I agree to Chris
Chris you give nice answers
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