By definition, the antagonist of any story is the character who goes against the protagonist, or the character who fights the hero. In this novel, Scout [or Atticus] could easily be considered protagonists. A simple way to ask this question is to say, "Which character goes against Scout [or Atticus] the most?" In order to answer the question for yourself, you should probably select one character as your protagonist.
Because of the length and complexity of this novel, there are several characters who could be considered antagonists. I am guessing your teacher does not have a specific answer in mind and wishes to hear your thoughts and ideas.
I would personally answer this question in a slightly more abstract way, than to simply name one of the other characters in the novel as the primary antagonist. I actually think that if you consider either Atticus or Scout as the primary protagonist of the novel, the strongest and most constant force against them is actually society. Several characters embody the different forms of ignorance, prejudice, and hypocrisy that Atticus is fighting, and subsequently teaching his children to fight as well. It seems the general attitude in Maycomb, the attitude that puts Atticus and his children most under attack could be summed up by the generic label of society. "Society" as an antagonist also allows for a very clear boundary of who is on Atticus' side and who is not. Miss Maudie, for example, though a Maycomb citizen, would probably be personally offended if she was included in the generic label of "society" here.
Another thing is Prejudice. If you want a charecter - I guess you could say Mr. Gilmer.
Scince I do not know what a antagonist is... I will have to say Atticus.