Ferbalot

A. One could aim for a country with a different education system that allows for much more logical people. If you have a populace made up of such people, they could effectively cooperate and strategize to protect people and keep them safe from government or enforce order within government. In such a scenario, the everyday people would protect you from government, and government would manage a military to effectively protect the everyday people from external threats. The military would also be made up of logical people (and if any attempt was made to change that, people would immediately recognize it as a massive threat).

B. Anti-anarchists could also answer with something like "no one could do these things very effectively, but its better than the chaotic alternative."

The methods for how a stateless nation could function effectively and avoid chaos are not immediately obvious, and there are arguments that at first seem to very clearly demonstrate that it's impossible.

C. "One part of government can keep you safe from another, and the other can keep you safe from the first."

A checks and balances system seems to generally be hard to maintain, but if it's possible to mitigate the advantage some people have via their power and money, it seemingly could be possible to maintain. That's easier said than done, but as an example of a semi-promising strategy...

Imagine you have ten departments, all with the same purpose:

a. Frequently check all the other departments for any monetary/power manipulation being used to alter the department's decisions, especially the more important ones.

b. Semi-randomly distribute some of the tasks that the government has been entrusted to take care of to the other departments. 

c. Work to complete the tasks assigned to it.

I'm not arguing that these answers are foolproof, but they're at least decently promising on the surface. The questions cannot be treated as knockout blows to anti-anarchism with the existence of such answers, in my opinion.