Destruction can be good or bad
I dislike senseless destruction, filth, and waste. That is one reason that when I celebrate "Random Acts of Anarchy Day" I usually do so by picking up litter, or by anonymously repairing something. The personality trait that makes me want to go around picking up litter is the same trait that makes me want to rid society of the state: I want to pick up the garbage that others have left behind and make the world a little bit better. I dislike the filth and pollution represented by, and spread by, statism. I realize that statists will continue to pollute society faster than I can clean up after them, and that most people don't yet recognize statism as the negatively destructive force it is. That doesn't mean I am spinning my wheels. After all, maybe I will eventually inspire someone who will make a real difference. Plus, I am far from alone; there are more of us libertarian/anarchists every day.
Of course, I also understand that every act of creativity begins with an act of purposeful destruction. You, or someone before you, must take something apart for the raw materials or constituent parts in order to create something new. The state could be dismantled and a better society, a consistent and rational society, could be built from the debris. There are a lot of intelligent people working for the state. Most could find honest work in a free society if they are willing to give up a life of coercion. There are a lot of guns owned by the military and "law enforcement" that could be better used in the hands of the general population; a population who would aim the guns at the right people - the aggressors and thieves. The day of the gangs (on both sides of the badge) would be over.