It really just isn't about the people vs governments however. Many anarchists will readily admit the state does some good for society and police aren't 100% corrupt and do help to a degree. What they do posit is the ends do not justify the means and there are more efficient means of organizing a society.
Anarchism posits a few basic principles that most people agree with with and follow in their personal life but make certain exceptions when it comes to corporations and governments:
1) Acknowledgement of property rights and self ownership
2) adherence to the non-aggression principle
Those 2 principles naturally have a consequence the social structure found within anarchism and Bitcoin - non-hierarchical, decentralized, free associations.
Once you understand this than anarchism isn't just antagonistic against governments, but also corporations who use the power of the state to enforce monopolies with patents , copyrights, and a limited liability veil, gangs who use violence to shake down people, and individuals who violently harass their neighbors or family.
We aren't proposing perfection just more consistent ethics which will lead to greater prosperity for all.