In a highly publicized kidnapping case in Ontario, the judge barred all media and spectators from the courtroom.
Local Citizens' Conclusion
These actions are inconsistent. rephrase: Pleading with the public to help find the victim contradicts not allowing the public to attend the trial.
Local Citizens' Evidence
Pleading with the public to help find the victim aroused the public interest. But they're saying that allowing us to attend the trial would not serve the public interest.
Evaluate
The citizen is finding a contradiction based on the concept of "public interest". Engaging the local citizens in the manhunt for the victim got them very interested in this kidnapping. So naturally, the citizen, is thinking, they are now very interested in attending / watching the trial.
How could the judge declare that the public interest would not be served by viewing the trial, if the public is so interested in viewing the trial?
There isn't any contradiction here. It's just two different senses of the term "public interest".
When we say that they pleaded with the public for help in finding the victim, thereby arousing the public's interest, we mean ... arousing the public's curiosity / intrigue.
When the judge says that allowing the public to attend this trial would not serve the public interest, she means ... it would not be good for the integrity of the judicial proceedings / it would not uphold the court's mission to deliver equal justice under the law.
Goal
Using the same term / concept in two very different ways is one of the ten famous flaws. The fancy word for it is Equivocation. But we often see answer choices alluding to this flaw (almost always incorrect answer choices, by the way), that simply say that the author used the term "X" in two different ways.