Anarchism, as a system based on cooperation, addresses the weaknesses in both liberal and conservative philosophies.
Like conservatives, anarchists think we should be taking personal responsibility for ourselves, our families, and our communities. But where conservatives want to put up a wall, beyond which their responsibilities don’t go, anarchists have always understood that resolving our problems requires taking responsibility on a worldwide scale.
Like liberals, anarchists are concerned with the vast majority of people who struggle to have even the basic necessities of life. But anarchists don’t want to install themselves in positions of power where they can met out drips and drabs of whatever liberals have been willing to give up. Anarchists want to work side by side with people, questioning the hierarchies and privileges that cause those inequities. We are not creating dependency, we are recognizing interdependency.
Looked at in this way, anarchism is nothing less than the ability to extend oneself in fellowship to others, regardless of their "political" views. It celebrates what is liberating about every perspective, and condemns everything that is not.