A second fallacy lies in the grammar. The answer "eliminate criminals" ignores the prepositional phrase of the statement "by treatment." Elimination is dependent upon the treatment. Really the original statement should be reworded: Treatment can eliminate cancer cells. Then, if the analogy of criminals being the cancer cells of society...
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A second fallacy lies in the grammar. The answer "eliminate criminals" ignores the prepositional phrase of the statement "by treatment." Elimination is dependent upon the treatment. Really the original statement should be reworded: Treatment can eliminate cancer cells. Then, if the analogy of criminals being the cancer cells of society is accepted (false analogy, though, they don't share enough qualities in commone), then the conclusion would be "Treat criminals", not "Eliminate".
Well, in many case more than one fallacy applies, but this one seems pretty clearly to be a weak analogy. Simply put, criminals are not the cancer cells of society, and the parallel is a weak one, leading to, as the final phrase indicates, false conclusions.