got corrected to
Why is it not possible to replace all of 好きな本 by の、given that the context makes the intended meaning obvious?
You could have said 僕は春の雪です instead, although this is colloquial and some teacher might still want to correct it, depending on their stance or your level of Japanese. This type of sentence is sometimes referred to as うなぎ文 ("eel sentence").
僕のは is wrong because 僕の refers to a thing that belongs to 僕. 僕のは春の雪です would sound like "My book is 春の雪."
１．「春の雪」です。This is good.
２．「春の雪」が好きです。This is good.
３．私は「春の雪」です。This is possible, as うなぎ文, but I don't like this. If I were a teacher, I would correct this if this is a person-to-person dialog. If there are plural people and they take turn to answer to the same question, this sentence is perfectly fine. It depends on the background.
４．私のは「春の雪」です。This is weird and unnatural, even though it seems not bad logically.
５．私の好きなのは「春の雪」です。This is okay. But I might prefer 6.
６．私が好きなのは「春の雪」です。 This is okay.
７．私が好きな本は「春の雪」です。 This is fine, but some people might say it's a little redundant.
８．「春の雪」が私の好きな本です。This is good.
９．「春の雪」が私は好きです。This is good.
１０．「春の雪」が私の好きなのです。This is weird, although it seems okay logically.
１１．「春の雪」が私のです。This is weird, although it seems logically okay.
I like the answers: 1, 2, (5), 6, (7), 8, 9.