What does the author mean by the following quote from paragraph 7, and how does it develop the central ideas of the article? : “when leaders attempt to navigate the slippery slope of fairness, they will find themselves arbiter of public opinion and hostage to the politically correct.”

What the author seems to be trying to say here is that there is always somebody that will be unhappy with what a leader has to say. 

In a healthy society, there are always opposing views that are designed to be discussed and debated at length. The eternal problem is that unfortunately, you can't please everybody.

Political correctness is a very controversial subject in that some people feel limited and unable to express views that may cause harm and damage to others. They claim that society holds them back from speaking their mind. It is very difficult to apply one definition to this concept as a whole because it is definitely influenced by your position on the matter.

It seems here that the question is designed to include your own analysis and a bit of your opinion, so be sure to add this as well as factual and generalized information.