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The EU is acting in the interests of the remaining 27 members. In this case it is specifically acting in the interests and on the instructions of the Republic of Ireland, which opposes a hard border under any circumstances.

The Republic of Ireland, and so the EU, are opposed to the UK having the ability to unilaterally exit the backstop as it removes any power they (IRE & EU) have to ensure that a hard border is avoided.

What's so important about the border? It's because dividing Ireland means an open invitation for a civil war again. The Troubles may or may not materialize again, but everybody would rather play it safe than find out.

EU doesn't want that. UK can't really be trusted they won't break the agreement that ended The Troubles, because some of the factions in power in UK act like they don't care about peace in Ireland.

Tying the backstop to the rest of the deal means that the deal is held hostage by the backstop. It basically sours the pot for the UK in case they consider bringing civil war back to Ireland. That's what makes it so attractive for Ireland, EU, and some in UK. Without the connection, UK could bring hard border back and retain eg. ability to import medicines from EU. With the connection, UK gets hit twice: once with risk inherent to hard border and secondly, with cutting down economic ties to EU (what makes the risk of eventual civil war even costlier, eg. without medicines to patch up SAS soldiers wounded in NI firefights).

Assuming that UK doesn't actually want hard border, they objectively lose nothing. The only thing they lose is face, because voters view it as giving up some options. And that's way more than it sounds, because the whole Brexit is about giving UK some options.

If either party can walk away unilaterally from part of an agreement, then what use is the negotiation in the first place? In this instance if the UK walks away from the backstop proposals unilaterally, this means there would not be a replacement agreement to deal with the issue of the Irish Border and the Good Friday Agreement (GFA), because by definition if there was such an agreement it would be bilateral.

The EU is concerned that allowing the UK to unilaterally change a part of the deal leaves the island of Ireland in a constant limbo with no clear picture of what state the border will be in next year, or potentially next week. Any change to conditions on the Irish Border risk the GFA and if done unilaterally would lead to a chaotic situation where it would be unclear under what principals goods and/or people could move across the NI/Eire border.

Why is the EU concerned about the UK “unilaterally withdrawing” from a backstop

I don't think that is an accurate description of the issue.

Backstop

UK Pro-Brexit MPs want a backstop to have a time limit or clear exit route. This is because they believe that locking the UK into the EU's customs union indefinitely would mean the UK could not have a meaningful independent trade policy.

The Irish government assert that the backstop cannot have an arbitrary end point but must apply unless and until some other political or technical development means it is no longer needed.

(paraphrased from https://www.bbc.co.uk/news/uk-northern-ireland-politics-44615404 - my emphasis)

Hard Borders

The UK government has said it does not want a hard border in the island of Ireland, so there is general agreement in the whole of the EU on that fundamental point. So far as I know, no major UK political party has proposed a hard border in the island of Ireland.

The BBC report

There is widespread agreement among UK politicians that there should be no return to what they call a hard border and that the Common Travel Area (CTA) should be maintained after Brexit.

Keeping agreements

The issue isn't whether the current or future UK government can be trusted to keep agreements it or it's predecessors have made.

If you don't trust someone to keep an agreement, you generally don't solve the trust issue by negotiating another agreement with them.

The point is to make sure that any agreement clearly and unambiguously meets the concerns of all parties to that agreement.

Unilateral withdrawal

So far as I know, governments only unilaterally withdraw from an agreement if the agreement provides for them to do so (but see Vienna convention below). For example article 50 of the treaty of Lisbon provides a mechanism by which an EU member state can arbitrarily and unilaterally withdraw from the union. It says "Any Member State may decide to withdraw from the Union in accordance with its own constitutional requirements"

So far as I can discern, the main pro-Brexit viewpoint is not that there should be a unilateral withdrawal clause to the backstop but that there should be a clause which describes the pre-agreed circumstances under which the backstop would become no longer needed to meet UK or IE concerns (e.g. perhaps a clear definition meeting the "some other political or technical development" of the Irish government's position).

The Irish Times puts it thus:

The breakthrough came with an agreement on a review mechanism that would determine when the backstop is no longer necessary to ensure that the Border remains open after Brexit.

The backstop is an insurance policy written into the withdrawal agreement guaranteeing no harder border on the island of Ireland. It would only be used as a last resort or the default option if the EU and UK cannot reach an overarching free trade deal that would make trade so frictionless that there would be no border between the EU and the UK, including on the frontier between Northern Ireland and the Republic.

Vienna convention

The Vienna Convention on the Law of Treaties states where a party wants to withdraw unilaterally from a treaty that is silent on secession, there are only two cases where withdrawal is allowed: where all parties recognise an informal right to do so and where the situation has changed so drastically, that the obligations of a signatory have been radically transformed.

The UK's unwritten constitution has the provision that current parliament cannot tie the hands of future ones in most cases. Therefore any promises made by the current government regarding the Irish border can only be enforced by international treaty, not merely by UK law (which can be repealed/amended unilaterally by future governments).

Many important points have already been made but one thing missing is that the backstop is emphatically not a transitional agreement. It's a fallback position if at some point in the future the arrangements between the UK and the EU fail to guarantee a border without physical infrastructure. It would not come into force in March 2019 when UK-Irish trade is still covered by the so-called “transition period” rules. In fact, it's not supposed to ever come into force, if you believe the claims that it should be possible to agree to some trade agreement that would deal with the border issue before the end of the transition period.

All parties want to avoid a hard border in Ireland, but the problem is that the UK also wants to be free to trade with anyone they want, even if that trade violates EU rules.

If the EU agreed to allow the UK to do this, and also allowed for there to be no hard border in Ireland, it would end up compromising the EU borders. The UK would be free to import goods from anywhere in the world, and then export those goods to the EU. The UK would essentially become a backdoor into the EU. It's pretty obvious that they cannot allow this situation to happen.

The UK want to have their cake and eat it. They want to both be part of the EU (no hard border in Ireland), and not part of the EU (free to make their own trade rules). These two aims are in direct opposition.

The EU is simply insisting that the UK stick to other commitments that it has made to EU members, in this case the Good Friday Agreement with Ireland. That agreement can only be modified with the consent of the voters of both the Republic of Ireland and Northern Ireland, the former of whom didn’t vote on Brexit and the latter of whom voted against it. If the Brexiters want a looser relationship with the EU while keeping the UK intact, then democracy requires that they convince those voters, not just the voters of England and Wales. Since they haven’t done so, then the UK must stay aligned with the EU in many ways to enable the border to stay open.