Many people will be puzzled. Why is the Northern Ireland (NI) issue so difficult to resolve in the Brexit negotiations?

When recently questioned about it, and the limitations NI imposes on the Brexit process, the UK Prime Minister gave a telling reply. It was along the lines that, as a sovereign country, the UK should have the right to leave the EU if it wishes to, and to do so without having to break up its component nations or create borders between them.

As with much that the Prime Minister says, the statement is superficially appealing (and guaranteed red meat for his supporters) but betrays an ignorance or avoidance of the underlying realities.

The basic fact is that the Good Friday Agreement and peace in Northern Ireland could not have been achieved had the UK not been part of the EU at the time.

Why? The Troubles in Northern Ireland have always been an issue of identity. Part of the population had a strong British (and Protestant) identity; the other part had a strong Irish (and Catholic) identity. Unionists or nationalists.

The strength of these different identities, and the fact that they had become opposed, cannot be underestimated. For instance, marriages between the two groups were referred to as mixed marriages and often caused problems. Symbols of identity (such as Orangemen marches) were often the focus of violence.

What the Good Friday Agreement – a culmination of many decades of work by many people – ultimately achieved was a way of minimising identity issues by creating a framework that allowed people to feel comfortable with choosing their own identity. This was achieved in many ways – not least the power-sharing agreement. But one crucial element was the freedom of movement of people and commerce on the island of Ireland.

Everyone should be honest in admitting that there is no solution that can maintain the current freedom of identity

People could cross the border, go shopping in whichever part of Ireland they wished, north or south, trade freely across the border and so on. To all intents and purposes, there was not much difference in people’s lived experience as they moved and interacted across the border. It was much easier for those with a nationalist identity to feel they were part of one island while those with a unionist identity were comfortable with still being part of the UK. It was all seamless in both directions.

None of this could have been achieved had the UK not been part of the EU – its single market and customs union.

Being part of the EU was, therefore, central to the Good Friday Agreement. Brexit shatters that concept. It is simply not possible to achieve the same freedom of identity outside of the EU. Either the unionists or the nationalists – or both – will have to give something up.

Boris Johnson, Leo Vardkar and other EU leaders are politicians. They are not magicians. However, any Brexit agreement is sliced, diced and put together again, it is simply impossible to achieve the same outcome in Ireland as has been achieved while Britain remains a member of the EU. This is a puzzle that has no solution simply because EU membership was an integral cog in the wheel of the NI peace process.

A withdrawal agreement that is acceptable to the Democratic Unionist Party (DUP) and other unionists may not satisfy the nationalists – and vice versa. Freedom of identity must necessarily be curtailed – either for one section of the population or for both.

The UK’s current proposal addresses this issue by curtailing some freedoms both for nationalists and unionists. There would be customs checks (away from the border) for goods moving between north and south. There would be regulatory checks between Northern Ireland and the rest of the UK as the UK leaves the single market. In that sense, the proposal is symmetrical in that both sides would be giving some ground if this agreement were to be approved.

It is, therefore, not an unreasonable framework provided it can be made to work in practice – which is by no means certain.

The EU’s counter that any future changes must be approved by representatives of the whole NI community – unionists and nationalists – is also reasonable. It is a principle of the peace agreement that one side should not be favoured over the other or have greater powers. Neither the DUP nor any other party that represents only one part of the NI community can be allowed to have a sole veto over future developments.

It is not clear if an agreement on the Irish border can be reached. However, everyone should be honest in admitting that there is no solution that can maintain the current freedom of identity. And no such solution can be forthcoming however long this issue is discussed.

Mr Vardkar and his EU partners must also be honest and admit that any asymmetric position they take that favours nationalists over unionists must be considered just as unacceptable as any position the UK government might put forward that favours unionists over nationalists.

When the EU is described as a peace project, it is usually taken to refer to peace in Europe after a long history of conflict between European nations. It is worth bearing in mind that, much closer to home and much more recently, it was also instrumental in bringing peace to Northern Ireland.

Joe Zammit-Lucia is a co-founder of Radix, the think tank for the radical centre (www.radixuk.org) and co-author of The Death of Liberal Democracy?