"That is not your thing."
Translation:Tio ne estas via afero.
When you ask someone their name you don't ask what they are, you know they are human, you are asking which specific human. I think that goes the same for other things.
Because you don't use the accusative if it is with "to be" -- "esti"
Mi estas kato - I am a cat. -- no accusative
Mi havas katon - I have a cat. -- accusative
Tio ne estas via afero - That is not your thing. -- no accusative
Vi ne havas vian aferon - You don't have your thing. -- accusative