Term for Exaggeration, Used in Argument

Solution 1:

Perhaps a "social knee-jerk reaction" may describe your situation with a mundane overtone.

Beyond your search for the "literary" term, ad hominem may be an interesting read for you. This phrase is also categorized under a neat diagram called Graham's Hierarchy of DisagreementGraham's Hierarchy of Disagreement

An axe-murderer refusing to do dish washing sits near the bottom, I must say.

Solution 2:

I think you may describe it as an overstatement :

  • something that you say that makes things seem more important, impressive or serious than they really are
  • making something seem more important than it really is: exaggeration, magnification.

A useful expression is also:

make a mountain out if a molehill:

  • Cliché to make a major issue out of a minor one; to exaggerate the importance of something. Come on, don't make a mountain out of a molehill. It's not that important. You wrote one bad essay - it doesn't mean you're going to fail your degree.

Source: www.macmillandictionary.com

Solution 3:

The direct opposite of 'hyperbole' ( overstatement) is 'litotes'; deliberate understatement.

In this context though, you've answered your own question. What you're describing is simply hyperbole.

http://en.m.wikipedia.org/wiki/Litotes