It's called freedom of speech. Flag-burning is a dramatic, if crude, method of criticizing the government.
Most politicians know that flag-burning is a form of free speech.
But hypocrites among them know they can gain more votes by pandering to the majority of unthinking people who don't understand democracy. The amendment is not the result of a careful study of an unmet legal problem. Rather, it is a reaction to a politically unpopular judicial decision. This idea comes around every year or so. The flag desecration amendment is not so admirable.