It means something close to your option (2): Fat can’t change into muscle, just like (as you may already know) muscle can’t change into fat. Regardless of its scientific correctness, this is the meaning that the phrasing implies.
Generally, phrases like “Eagles cannot swim any more than sharks can fly” are an idiomatic construction. They essentially always mean Eagles can’t swim, just like (as you may already know) sharks can’t fly — or in more detail:
- it’s impossible, or very unlikely, for sharks to fly (and this is usually assumed as likely background knowledge for the writer and reader);
- and it is similarly unlikely for eagles to swim (and this is the main new information the writer is giving the reader).
This phrasing is always used to express impossibility/unlikeliness like this — it does not just mean “ability of eagles to swim ≤ ability of sharks to fly”, as a literal logical reading would entail. For instance, one would never naturally say or write the following, even though strictly logically they’re true:
- *Eagles cannot swim any more than dogs can walk.
- *Eagles cannot fly any more than dogs can walk.
And slightly more subtly, the first impossibility is the main new information being asserted, while the second one is typically presumed as background knowledge; so one would not say
- *Pigs cannot fly any more than elephants can jump.
because although both of these are impossible, readers can be assumed to know the first impossibility more than the second.