Statist: Without government, society would descend into chaos.
Anarchist: Historically and today, there has been no greater agent of chaos, disorder, violence, and lawlessness than coercive government. No private concern has ever or could ever match the government's anti-social effects on society. When free of a coercive agent, humans (as social animals) tend to cooperate and organise in self-interest and concern for others. The corruption so common in government agencies and institutions that stems from possessing a coercive monopoly can be regulated by competition in non-coercive market counterparts to such institutions (courts, security, etc.).
Statist: You seem to trust people in theory more than you would in real life. Real people are inherently evil; therefore, we need government to keep them in line.
Anarchist: Government is made up of people. If people are inherently evil, the worst thing that could happen is for a small group of them to seize and maintain a monopoly on crime (unjustified use of violence). I definately don't trust people with that.
Statist: I just can't imagine how a society could function without government. It just all seems a little "pie in the sky".
Anarchist: There was a long period of time when people simply could not imagine how society could function without the church, or how economies could function without slavery. These are ancient institutions with rigorously taught mysticisms. It takes time, study and reflection to be able to imagine a world without them.
Ultimately the world always changes and the people change with it. We have to strive collectively to change it into a world better suited for happiness. It is up to us to culturally determine what the next generation sees as neccesary and good and anarchists want posterity to live in a world of freedom, equality, and solidarity.
Statist: Umm . . . I see, yes. I admire your idealism but, WHO WOULD PAVE THE ROADS!?!?!