That's your bias

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Saying "That's your bias" (or other words to the same effect) in response to a reasoned argument is basically a form of argument from subjectivity combined with an ad hominem:

  • argument from subjectivity: claims the matter is too subjective to be resolved by rational discussion
  • ad hominem: claims that the defender is biased on this subject, implying that they are incapable of reasoning objectively on the matter. This makes it effectively impossible for them to make any argument that cannot be similarly shot down.

It is similar to "That's your opinion", but with the additional ad hominem implication.