I think the main barrier to anarchism is removing, as much as possible, the cultural herd instinct (which I personally think has a genetic component) toward hierarchy, especially authoritarian and permanent hierarchies (as opposed to fluid, context-specific hierarchies as one might expect to see appearing and dissappearing in a anarchism). Basically people have become used to, in fact are conditioned into, accepting authority on an arbitrary basis (Why can't I do that? 'Becuase I'm your parent/teacher and I'm telling you you can't) but also because in doing so, lots of responsibility for ones life, for the choices one makes, are taken away - often these choices will be diffilcult to make, but also it frees people up from responsibility. One of the great capitalist corruptions of environmental arguments about behaviour is that at some point the concept of personal responsibility and decision making dissappeared. A 16 year old who breaks in to an OAPs house, robs her and rapes her may well be a product of his environment, but his actions are still his responsibility, not a mechanistic, deterministic, robot-like 'I have had a hard life therefore I must do these things'.
For me this notion of being absolutely responsible for ones actions, and accountable to the wider community for them, coupled with a lack of 'leaders', are the things that really scare people about anarchism. I mean think about it - you live in an anarchist society and something goes seriously wrong - harvest failure for example - there aren't any politicians to blame, there aren't any authority figures, it's a genuine collective failure that could have dire consequences.
So to sum up -
Our societies have been built around coercive, arbitrary authority for such a long time that it's so rooted in our cultures as to be almost instincual.
Anarchism would mean having to accept responsibility for ourselves completely, and for any wider failures in society
Anarchism would be seriously fucking hard work for at least 2, possibly 3 generations - how do you deal with reactionary thinking without compromising your own anarchist beliefs (I have a plan for this but would mean those involved would ultimately sacrifice their own choices and freedoms because the actions required of them would be reactionary too)
And the only crime in such a society would be the brilliantly succint invention of China Mieville: Choice Theft