Here's why:
* Subject: The subject of a sentence is the person, place, thing, or idea that performs the action of the verb.
* Verb: The verb in this sentence is "is" (understood, but implied).
* "My favorite fish" is the subject.
* "Swordfish" is the predicate nominative, which renames the subject.
The sentence is a fragment and would be more complete as: "My favorite fish is swordfish."