In this case fish is a noun. Pronouns are words such as you, me, he, she, and they. Catching is the verb, oldest is an adjective, and pastime is also a noun, but not the subject of the sentence. The word fish can be used as a verb in a sentence like "They taught me to fish."
Actually, I think it is a NONE of those options you were given. If it were a noun then "catching" would be a modifier, and thus an optional component of the sentence. But if we remove it we are left with "Fish is one of the oldest pastimes" which is ungrammatical. Instead "fish" seems the optional component to the sentence, and is thus a modifier of "catching" since the sentence "Catching is one of the oldest pastimes" is still grammatical. It appears to me that "catching" is in fact the noun; "fish" modifies the noun, and is in fact an ADVERB.
Another similar example is of the word "home" in "I am going home". At first glace one would think home is a noun, but it is an adverb.
