Analogy is a powerful tool in reasoning.
An analogy can nearly always be extended "ad absurdum" by an contrary listener. The purpose of analogy is thus misunderstood.
In some cases, the purpose is to allow a point of view to be considered without the emotional baggage and pre-judgement ("prejudice") that accompanies the original context.e.g. let's imagine that you come home and find another family in your lounge. Many people can honestly evaluate their reactions to this event because there is no learnt "politically correct" response. They can agree that feelings of anger may be felt, may indeed be justified. They may not agree to let the family stay despite hearing their sad story and hearing them threaten to take desperate measures. Indeed, the more desperate the story and the threats, the more frightening the prospect of allowing them to stay. Now, imagine that the family in your lounge were anglo-saxon Australians !Such analogies allow reflection on some aspects of a situation that otherwise would never be rationally considered. Of course, all analogies have limits.
Analogy, can of course be used to raise the emotional stakes and cloud rational judgement as well. One of the most frequently used contexts for this purpose is the Nazi party.e.g. So you want me to wear a uniform.... just like the Nazi's did. etc etc.
But there can be more subtle contexts which play on multiple emotions. E.g. when discussing educational funding analogies and examples can bechosen to build on the guilt people may feel for their own privileged education; the envy of those who were educated at poorer schools; the anger at governments that squander public monies on educational systems with so little reaching the schools and classrooms; the powerlessness parents feel in the face of schools that are responsive only to the governments that distribute public funds - but not to their local "public".
Multiple simultaneous analogy is also useful to highlight the complexity of a situation. This is frequently used in science where polemic is usually less acceptable and the only constant is uncertainty.e.g. the behaviour of light follows mathematically formulas based on an analogy with tiny imaginary particles. It also simultaneously obeys rules based on an analogy with waves.
Taking an analogy to absurd lengths does not illustrate its failure. It merely illustrates the reluctance of the listener to to stand outside the prejudice and explore another viewpoint.Decisions in politics, the courts, and in life are made on the balance obtained by giving different weight to a variety of rich analogies