Red herring
A red herring is when you bring up a different topic so people forget what was actually being discussed. You distract from the issue instead of addressing it. The new topic may be related or emotionally charged, but it doesn't answer the original question or objection. The fallacy is to shift attention away from the relevant point. Spotting it means asking: does this actually respond to what was asked?
Examples
Why did you vote for that rule? — Well, the other side have done much worse things.
Did you finish the report? — I've been really busy with the new project.
How do you justify the cost? — Our competitors are spending even more.
Was the decision fair? — Look at how hard everyone has been working.
Why did you miss the deadline? — The client changed the scope.