Which logical fallacy is used in the text?
How could I possibly have time to wash the dishes when so much carbon dioxide is being spewed into the atmosphere on a daily basis?

 - red herring: the use of a completely unrelated topic or idea
 - false dichotomy: an argument that presents only two choices when more options exist
The text argues that carbon dioxide entering the atmosphere somehow prevents the speaker from washing the dishes. However, these two ideas aren't related. This illustrates a type of logical fallacy known as a red herring.