Some battles become unwinnable the moment you agree to fight them.

Certain conflicts are structured so that participating is the loss, regardless of outcome. Public arguments with someone who is comfortable being unreasonable work this way, since they lose nothing and you spend your credibility and your calm. Agreeing to fight is the decisive move.

Before engaging, ask what the other person is risking. If the answer is nothing, the contest is not symmetrical and winning is not available. Declining is not avoidance in that case, it is accurate assessment.