"Anarchy" does not mean chaos and disorder. It does not mean people looting shops and killing each other in the streets.
Anarchy isn't about violence and coercion, except in the negative. Anarchists aren't -for- those things. They're -against- them, especially at the scale with which they are practiced by governments. Governments are the largest murderers, thieves, and coercion specialists in the world. As long as there's been government, there's been massive death and destruction of wealth and well being.
Inevitably, people will say, "but without government, how will we do x?", and present that with the full expectation that a lack of an answer to their question requires a default acceptance of the morality of the evils done by the people in government. But even if that -were- the case(which it is not. It is a question of morality, not a question of what's most useful to you), the simple answer to that question, regardless of the value of 'x', is, "However it was done before government took control of it and started fining, imprisoning, and killing anyone who did it without their permission.
Anarchy isn't about disorder and death.
Anarchy is about the naturally occurring order of people working together to achieve goals that advance their own individual self interest.
There has never been an anarchist who has commanded armed forces to kill, occupy, or steal from others. Governments do that every day. We only want that to stop being venerated and applauded by society.
I'm sure that may be what you want, but a utopian society where everyone gets along, and is nice to each other, with no rules or authority, is not possible.
Sorry, but anarchists don't believe in a utopian society. If anyone, pro government people are the ones who believe in utopian societies. Anarchists point out that society IS flawed, and power structures ARE flawed, and thus, should not be given immense power over great swathes of people, especially powers like death, imprisonment, and the ability to command payment.