One popular criticism of anarchism is to point to the violent civil war going on in Somalia, and say that this is what happens when you have anarchy. Anarchists are of course used to this, and clearly we disagree or else we wouldn't - at least in general - be anarchists. I can imagine that there are some who take an extreme "government should not violate rights, regardless of the consequences, and if that leads to a Hobbesian nightmare then at least we are morally beyond reproach" line, but am personally confident that somewhere along the line I would be happy to give up rights if that were necessary to preserve a civilised society. There's a discussion of Somalia currently going on in the Anarcho-Capitalism subreddit, which led me to do a bit of reading up on the subject. This is my attempt to present the various arguments used.
(1) The war was caused by the state, in a particularly bad consequence of the fall of communism. Observe that all of the warlords, at first, were generals in the Somalian army before.
(2) Warlords are government - they violate the non-aggression principle as surely as any state.
(3) Somalia isn't really anarchy - it's a bunch of small states, all of whom happen to be at war with one another.
(4) Somalia really isn't as bad as we think - compared to other African countries, it is actually doing pretty well.
(5) Within any political system there will be nations which do better or worse within that system. Somalia is likely a particularly bad example of anarchism, and comparing it to developed countries (as tend to be done is grossly unfair). The best comparison would be somewhere like North Korea, and for all its violence most people would rather live in Somalia than North Korea.
(6) A functioning anarchy requires people to understand and accept anarchism - it cannot simply develop out of thin air. (I'm not presenting this well here, see here for a short but well-written exposition of the argument).
Without commenting on the force or truth of any of these arguments (hint: I agree with some but not all - in particular, (2) just seems like an attempt to redefine the word 'government' to include anything we don't like) it seems to me like there is a split between these arguments: arguments (1), (2), (3) and (6) all seem to say "Somalia isn't truly anarchist" whereas (4) and (5) say "Yes, Somalia is anarchist, and it really isn't so bad." There isn't necessarily a contradiction - you could probably argue that anarchy developed out of a failed state - but in general it seems like these are two different conclusions being argued towards, and the combination of the two - "The violence in Somalia is because they have a government, and because they're anarchist they're actually doing better than other countries in their situation" - is flat out contradictory.