Anarchy means no rulers, therefore no slaves.
The only difference between what we have now and anarchy is a free market in government where everyone pays for and uses the services they want and/or believe in, and is not forced to support things they don't want or believe in.
Anarchy doesn't mean we don't protect against murderers and invaders, it means the ways we do those things doesn't involve forcing people who dislike our methods to participate and support our way of doing it.
People think anarchy means no organizations. There would be organizations, but they would be voluntary membership. Everything we do now which statists claim is necessary (rightly so in many cases) can exist in a non-coercive form, and they'll be better than what we have now because of free market competition.
Anarchy means the right to consent.