The answer is: [C]: "<span>an infinitive phrase as the subject" .
________________________________________________________
The infinitive is: "To win" .
_________________________________________
The infinitve phrase is: "To win an argument" .
_________________________________________</span>
The appositive is a renaming of a noun, something that can be skipped without changing the grammatically and meaning of the sentence.
Here the appositive is "Dr. Walters" - it can be skipped:
My dentist was one of the speakers at Career Day
and it renames "My dentist" - answer B