Homosexuals must not be allowed to hold government office. Hence any government official who is revealed to be a homosexual will lose their job. Therefore homosexuals will do anything to hide their secret, and will be open to dishonesty and blackmail. Thus, homosexuals should not be allowed to hold government office.
Which fallacy is this?
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Fallacies This handout is on common logical fallacies that you may encounter in your own writing or the writing of others. The handout provides definitions, examples, ...
http://www.unc.edu/depts/wcweb/handouts/fallacies.html
Fallacies 42 informal logical fallacies explained by Dr. Michael C. Labossiere, including examples.
http://www.nizkor.org/features/fallacies/