The easiest way to understand anarchy is to start with morals. And most morals can be boiled down to:
"Don't harm others. Unless they harm you first."
Christianity takes it a step further: "Don't harm others. Period." But pretty much every religion, culture, and nation agrees on the first one. Some people came up with a fancy term, and called it the "non-agression principle". Most other people just call it being a decent human being.
I think it's legitimate to question whether you want to be moral or not. But if you do want morals, then you have to apply them universally. If you apply some morals to yourself, and different morals to others, you're no longer moral, you're just discriminating.
But if morals apply universally, to everyone exactly the same, then there can be no government.