I've seen the following scenario played out again and again in online discussions: An observer notices a blatant contradiction in someone's worldview and calls them on it. Instead of being floored and addressing their own hypocrisy, the subject make a lazy deflection and declares a false equivalence is afoot.
False equivalence means the two things being compared are actually not comparable. Sometimes they come with an explanation, sometimes they don't.
Click the following cartoon and be reminded that arguments are much easier to win when you write the script for both sides:
...And they're harder to win when a critic adds a zinger at the end.
Of course people really can make bad comparisons. Drone strikes are not the same as housing construction ordinances. Driving faster than the speed limit is not the same as breaking child pornography laws. Opposing the abortion of an unborn child is not the same as opposing the execution of a convicted killer.
Sorry guys, it's really not.
But when people want to hold on to a real contradiction, such as believing that female fitness models shame women while male fitness models don't shame men, they engage in a form of special pleading by declaring that the comparison is bogus because of some strained, trivial difference.
Be careful when one claims an opponent is making a logical fallacy; you could be making one of your own.