You seem to think that Anarchism is just the extreme/pure form of Libertarianism, and that it's just about more/less government, which couldn't be further from the truth.

I'll acknowledge my bias upfront, I consider myself an Anarchist, so keep that in mind as you read my comment.

American Libertarianism presents itself as being about "small government," which makes it sound appealing to people who are skeptical of authority but have a very shallow understanding of politics. In truth, it's an ideology that holds individual property rights as superior to all others. To an American Libertarian, any infringement on their property rights is the most egregious possible violation of their freedom.

Anarchism means "without rulers." Anarchists oppose all forms of exploitation and oppression, which is described as any arrangement in which one person or group exerts authority over another person or group, usually by force. They favor organizing society via "voluntary free association," which is when people make decisions together on the basis of general consent. To an Anarchist, private property (as opposed to personal property, there is a distinction) is just another way for someone to exploit another, such as when a landlord collects rent.

This text explains what anarchism is pretty well.