I’ll do my best, けど…
Breaking down the sentence, we have:
学生 - student
で - location particle
いる - to be, to exist (animate objects only)
の - possessive/explanatory particle
が好き - is liked (set phrase)
です - copula
So, the sentence has the literal meaning of: “(The concept of) being a student is liked (by me).” Even if we didn’t know what the で particle does here, we can infer that「学生でいる」means “to be a student” (lit. to exist at student), and combining it with「が好きです」, a set phrase meaning “is liked”, we see that the full phrase is literally translated as above. According to Tae Kim, the の particle can be used as a nominalization tool, like mentioned in your post. From lesson 3.11 (page 65 of the physical version):
The 「の」 particle in this usage essentially replaces the noun and takes over the role as the noun itself. We can essentially treat adjectives and verbs like nouns by just adding the 「の」 particle to it. The particle then becomes a generic noun, which we can treat just like a regular noun.
I’ve bolded the key phrase here. What’s important is that the の particle is turning the entire phrase before it; 学生でいる, which is a verb phrase; into a noun. This is because が好き can only be used with nouns.
As a side note: I don’t actually know why 学生だのが好きです is wrong. I would appreciate it if someone with more expertise could help me out.
Edit: I just got Leebo’d, god dammit. Look at the above comment.
Hope this helped, and welcome to WaniKani!