Still working to recover. Please don't edit quite yet.
Anarchists believe that hierarchical authority is illegitimate. They believe that everyone should have the maximum number of rights and freedoms. Illegitimate authority is seen as unethical because it is imposed on others without their consent, and so is coercive. Coercive force is unethical. Such authority benefits the elite at the expense of the non-elite. Anarchists distinguish between legitimate and illegitimate authority. If two people are having a dispute and agree to take it to a judge to be resolved, then the ruling of the judge constitutes legitimate authority. Any institution (or people) who takes it upon themselves to enforce their "authority" on others without consent is illegitimate. Government constitutes an illegitimate authority because they have a monopoly on force, and one is not given a choice whether or not to be considered to be under their jurisdiction. In most countries you would be free to leave, but you would simply be moving from one illegitimate authority to another. Anarchists want to be free of illegitimate authority. Popular self rule is the only legitimate authority in society. Anything else is maintained by force, the antithesis of reason.
Ethical anarchist society
In an ethical anarchist society, everyone would grant equal rights to each other. Everyone has the right to do what they want so long as they don't infringe on the rights of others. This means no one would have rights that would infringe on the rights of others. If you have the right to life, someone else can't have the right to kill you, even if they have the freedom to do so. By infringing on someone's rights, you're demonstrating a lack of respect for that right, and effectively relinquishing your same rights, since the person so infringed upon has no reason to respect your rights if you obviously don't respect theirs. Do unto others...