These are some examples of how people try to avoid the initial question or discussion:

• Red Herring Fallacy
• Debating Using the Exceptions to the Rule (Special Pleading Fallacy)
• Attacking the Messenger (Ad Hominem Attack)
• Genetic Fallacy or Origins Fallacy or Fallacy of Virtue
• The "You Too" Fallacy or the Tu Quoque Fallacy
• The Faulty Appeal to Authority 
• The Appeal to the People Fallacy.
• The Straw Man Fallacy.