A common refrain as the Brexit crisis unfolds is that not only is the United Kingdom’s Brexit process in a fine mess, it was one that Theresa May’s government got itself into. Government incompetence got us to today, with little progress, and a worryingly high chance a disorderly jettisoning from the European Union.

Labour - and in particular Keir Starmer - naturally adopt this posture, understandably seeking to maximise political capital from the debacle. But other disinterested commentators join in. It hardly seems right to single anyone out, as this is a common refrain, but David Allen Green’s blog and columns adopt the view constantly that this was a process that could have been done well with the right degree of administrative acumen.

What those who push this view downplay is that the most important difficulty all along has been how to reconcile the competing desires of the different factions either in favour of Brexit all along, or now seeking to make the best of it. They think of the government (and the Opposition) as single, strategizing entities, and deduce from the chaos that they must be bungling. The reality is that we have two debates, not a government and an opposition.

The irreconcilability within government ranks was almost inevitable given the design of the referendum question, which did not specify anything about what the UK should leave to. No doubt without this ambiguity, there would have been less support for Leave, since as it was a very broad church could be united. So we can say that the very fact we are embarked on Brexit at all means it was highly likely to be warfare afterwards.

Key amongst the congregation of the Leave Church were: ‘liberal leavers’ who wanted to leave the single market and create open borders and free trade with the rest of the world; liberal leavers who wished to stay in the single market and retain symbolic control over sovereignty, accepting that for now this was the freest trading circumstance possible; those who wanted to de-globalise, intervene more in industry, reduce migration, ‘take back control’. And perhaps other factions with darker motives, too.

It is not incompetence to have failed to reconcile these inconsistent viewpoints. What has to happen to move forward is that all but one of the factions has to submit, or be forced to in favour of a winner. It is fairer to suggest that it was bad politics to end up without the political power simply to ignore or squash those factions except for your own, as Theresa May has done.

But even this could be excused to some extent. She picked the kind of Brexit that seemed to command a majority of her party, hoped to extend that majority to be able to dispense with the ex-Remainers, and lost ground because key swathes of tactical voters did not like it. May is not able to send one faction packing because the nation is also undecided on the post Brexit future.

Part of the difficulty is that there is a degree of binariness foisted on the UK by the incentives facing the European Union itself. Without this, it would be easier to sit Brexiters and Remainers down to do a bit of old fashioned horse-trading.

For the EU, Brexit is part of an existential crisis. Existential because of a list of other threats: the Mediterranean refugee crisis, albeit now abated; an unfriendly and protectionist United States; an unfriendly and meddling Russia; populist governments in Poland and Hungary; a financially unstable Italy; not entirely vanquished populist movements in Holland, Spain, Greece, Italy and France.

These issues raise the stakes for the EU. Presenting the UK with a neat set of options all the way from the status quo to a Hard Brexit, with varying degrees of regulatory alignment, trade openness, and migration is not possible. Many of the possibilities, like trading under existing terms but without freedom of movement, or applying the single market to some sectors and not others, can’t be offered for fear of sparking a desire on the part of other members to renegotiate their own relationship with the EU. So the EU has tried to present us with a harsh sounding In-or-Out choice.

This confronts the UK cabinet with options that are very far apart, and so neither side relishes what would amount to a capitulation and won’t give in until the last possible moment.

Appeals to competence and ‘leadership’ (Nick Macpherson, former Treasury Permanent Secretary chose that word) are sentimental and unrealistic. As though charisma and get-go could dissolve fundamental ideological disagreements.

One genuine question of competence is the worry that not everyone who matters in the argument understands what is and is not feasible given the EU’s predicament. Or has an even approximately sensible notion of the costs and benefits attached to the different options.

Some of the public statements by the participants suggest that their understanding of these things is wanting. There are countless examples of the Brexit Ultras saying things that imply they want their ‘cake and eat it’; meaning they want their regulatory divergence [sovereignty cake] and frictionless trade [the eating it] at the same time. There are fewer, but still worryingly frequent interventions by others from that constituency seeming to welcome the most disorderly, abrupt and Hardest Brexit.

Taken at face value, these interventions are daft. But seen as a part of a fight to the death with Remainers, it is more explicable.

Perhaps those speeches are the result of the same kind of diabolical calculation made by Dr Strangeglove of the Kubrick film by the same name, whose seemingly crazy sabre rattling with nuclear weapons was designed to make the Soviets back down. They could be aimed at provoking the following calculation in the minds of the moderates: ‘They really believe this cake and eat it stuff, don’t they, despite evidence to the contrary? So they are not going to back down. And if we are to avoid the disaster of disunity in the negotiations, or have a chance of picking up the pieces at some point, perhaps we should back down now and let the other lot take a run at it.’

But what about Article 50, goes the main accusation from those who feel this is all about competence. How could you start the two year clock ticking to either a hasty withdrawal agreement or bust without having figured out what you want? How could Labour whip its MPs to support that? Isn’t that reckless?

Well, once again you have to drop the idea that either side consists of single thinking units in control of all their own moving parts. If this is a game of chicken between starkly opposing factions, more time is not productive, since neither will back down anyway until the last possible moment.

The chaos of Brexit is not primarily matter of administrative missteps. It is inherent in the ambiguity of the Leave vote; the radically divergent and conflicting visions for Britain’s future outside the EU; and the incentive the EU has to preserve itself by offering us binary choices, which make Leaving for others look very bad.