Word/phrase/idiom to describe avoiding answering a question by stating the question doesn't need to be asked

Solution 1:

One relevant term from logic:

red herring — The idiom "red herring" is used to refer to something that misleads or distracts from the relevant or important issue.

Specific forms of red herring exist and I find that appeal to motive fits nicely:

appeal to motive — Appeal to motive is a pattern of argument which consists in challenging a thesis by calling into question the motives of its proposer. It can be considered as a special case of the ad hominem circumstantial argument. As such, this type of argument may be an informal fallacy.

The person who answers that you should go to Burger King instead is assuming that your motive for asking the question is that you want to get something to eat. This is an invalid assumption and, therefore, their answer is completely irrelevant.

More informally, this pattern of behavior is simply known as "dodging the question":

dodging the question — Question dodging is the intentional avoidance of answering a question.

On that wiki page they have a list of example forms and these seem particularly apt. In response to the question, "Why are you here?":

• Answering things that weren't asked ("I'm in the corridor.")
• Questioning the question ("Are you sure that's relevant?")
• Challenging the question ("You assume I am here for a reason.")
• Giving an answer in the wrong context ("Because I was born.")

The motive for dodging the question in your example is that they don't know the answer. Thus, they answer a different question.

Solution 2:

You might consider this as a case of ignoratio elenchi, where an irrelevant argument is presented as an answer to the question at hand:

Ignoratio elenchi, also known as irrelevant conclusion, is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question.

[...] The nature of the fallacy, then, consists in substituting for a certain issue another which is more or less closely related to it, and arguing the substituted issue.

It seems a little grandiose for what you're describing but is a good fit nevertheless.