Nice analysis of this by Emily Jones and Calum Miller of the Blavatnik School of Government in Oxford. Summary:

The country’s leaders need to accept that the primary objectives of Brexit are, and always have been, mutually incompatible. Sadly, their refusal to acknowledge this is indicative of the kind of leadership that led to the current impasse.

With the European Union’s latest extension of the United Kingdom’s membership in the bloc, onlookers around the world are right to wonder why the Brexit process has proved so intractable. The short answer is that the UK’s government and parliament are trying to achieve three incompatible goals: preserving the country’s territorial integrity, preventing the return of a hard border between Northern Ireland and the Republic of Ireland, and enabling the UK to strike its own trade deals.

The British are finally confronting the fact that only two of these objectives can be met at any one time. This implies that there are three basic scenarios for moving ahead with Brexit…

Worth reading in full.