The man who invented Western philosophy, Aristotle, considered ignoratio elenchi,
 which roughly translates to "irrelevant thesis," an umbrella term that 
covered all other logical fallacies. Indeed, most of the other fallacies
 on this list could be categorized as subsets of the irrelevant thesis. 
Formally, ignoratio elenchi refers to any rebuttal that fails to address the central argument.
And for those who are searching for an example of ignoratio elenchi, look no further than the presidential debate between President Bush and Senator Kerry. What transpired during the event happens with almost every question asked in a political setting. For example, at a televised debate between presidential candidates, 
the mediator might ask, "If you become president, what would you do 
about the rising unemployment numbers?" to which the candidate might 
reply, "I'm glad you asked, because unemployment is the greatest problem
 facing this nation yadda yadda yadda, and my opponent's plan to deal 
with the problem is completely insufficient." Notice, in this example, 
how the candidate dodged the question entirely. He made an argument, but
 it didn't answer the mediator's concerns and was thus an irrelevant 
thesis.
Another example of ignoratio elenchi is the "two wrongs make
 a right" fallacy, which was recently used to great effect by the 
Democrats during the final stages of the healthcare debate. When asked 
if he thought using the reconciliation strategy to pass the healthcare 
bill with a simple majority vote was the right thing to do, Senate 
Majority Leader Harry Reid--after claiming that nobody was talking about
 it (a logical fallacy known as the incorrect statement)--Reid released a
 statement detailing how many times the Republicans have used the 
reconciliation strategy over the last decade. Like the example above, 
Reid made an argument, but it was an irrelevant one that said nothing 
about how right or wrong the strategy is.
This kind of thing happens in cycles, because the majority party is 
always changing hands. When the minority party is called childish for 
filibustering a judicial nominee or something, for instance, they always
 come back with something along the lines of "You guys did the same 
thing a few years back, nanny nanny boo boo!" This is, of course, a 
meaningless argument, even though it is usually true. Even if your 
opponent shot somebody and got away with it, it doesn't mean you can do 
the same thing.
I liked your argument and examples, and found it especially relevant as you brought up the fact that both parties do it. American politics are riddled with fallacies and no one seems to consider that its the system, not the people.
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