Whataboutism is a highly informal term used primarily in politics to refer to a whole slew of fallacies, including ad hominem, tu quoque, argument from fallacy, and the fallacy of relative privation. It consists of bringing in thematically related events, statements, and actions to deflect attention from the central issue.
"Whataboutism: The practice of responding to an accusation or difficult question by making a counter-accusation or raising a different issue. Also in later use: the practice of raising a supposedly analogous issue in response to a perceived hypocrisy or inconsistency."
-- The Oxford English Dictionary
As this definition suggests, an accusation of whataboutism is leveled in cases where it is believed to be inappropriate; if you believe that the challenge is fair you might call it a counterexample, a counterpoint, a challenge, an analogy, or an intuition pump -- but surely nothing so foul as whataboutism. If a charge of whataboutism is leveled, it indicates that at least one side of the debate has jumped the tracks, and unless you have the utmost confidence in your conversation partner it is time to give up. However, if you do wish to continue the debate the proper way to meet the challenge is to recenter the conversation on what general rule or principle should apply to all sides, and shift the debate to that.