The argument appears to boil down to: the situation under the current Protocol is unsustainable, the British government feels that it would be entitled to invoke Article 16 of the Protocol, allowing it to unilaterally take action, but would prefer to proceed bilaterally with the EU to come to an agreement which both sides can be satisfied with.
The government's position on the renegotiation of the Northern Ireland Protocol was set out in a statement made simultaneously in the House of Lords by Minister of State Lord Frost and in the House of Commons by the Secretary of State for Northern Ireland Brandon Lewis.
The main argument presented in the statement is that the negotiations on the agreement took place without true knowledge of "what the real-world impacts of those decisions on the ground would be", which the statement notes include the need for half-a-billion pounds to be invested in implementing the agreement, and knock-on effects on the supply of goods from Great Britain to Northern Ireland.
Another argument presented by the government is that the existing procedures within the protocol have been exhausted - the statement notes that "avenues for progress have been identified in certain areas but, overall, those discussions have not got to the heart of the problem". The government, however, states that it is unwilling to use the provisions of Article 16 of the Protocol - which allows the UK and the EU to take appropriate safeguard measures in the case of "serious economic, societal or environmental difficulties that are liable to persist, or to diversion of trade" despite arguing that "it is clear that the circumstances exist to justify [its] use". It argues instead that rather than have the relationship between the UK and the EU be defined by legal challenges and power struggles over Northern Ireland, it is more constructive to renegotiate the agreement to the benefit of both parties.
Full details of the government's position are set out in the Command Paper entitled Northern Ireland Protocol: the way forward. The foreword by the Prime Minister sets out similar arguments made in the statement made in parliament, but section six; "Next Steps" is also quite digestible - the argument is presented that the UK has a responsibility to Northern Ireland as a co-signatory of the Good Friday agreement, and it is also recognised that there is a desire within the EU for the peace process in NI to be supported. The paper argues that the best way to ensure that this continues to be the case is through renegotiation of the Protocol;
The best way to do this is through finding new and durable
arrangements agreed by the UK and the EU together, in which there is
a shared ongoing interest in their success. This will best serve
businesses and citizens in Northern Ireland; and provide the
strongest platform for the productive long-term relationship between
the UK and EU that we all want.