An obligation is created independent from a contract and can legally persist if the contract is terminated. If I were to take out a loan with my bank and sign a 10-year contract to pay it off, but then decide after 2 years that I want to terminate that loan contract early, my obligation to the bank to pay off the loan still exists, even if there is no longer a formal contract between us.

This is a terrible example, and actually contradicts your claim that an obligation is created independent of a contract. In your example the obligation is created BECAUSE of a contract, and you haven't actually ended your contract at all with the bank, because you can't until you have met the obligations of that contract (paid it all back) You can't actually terminate the load contract early without fulfilling the obligation to pay as the obligation is entirely what the contract is about.

Legal Obligations either come from Laws which apply (which international law does not cover in this situation, and international law is not binding like national law as it lacks a powerful enforcer, so frequently gets ignored by countries so is much more about general reputatation and agreement than it is like actual laws.) or from contracts. The EU budget is not a legally binding contract on anyone except current members of the EU, most likely is the legal position of the UK. If it was something the EU thought was legally binding on the UK, they absolutely would have said so by now. The lack of referring to the UK's divorce fee as legally obliged shows they know it is no such thing.

They are purely trying to argue it on the basis of morality, and on the basis of international reputation, and on the basis of ongoing friendship.

The UK agreed to do things as part of the EU, if it isn't going to be part of the EU anymore then how much further it does those things is absolutely on the table. If the EU is going to be a dick to the UK and create a punishment deal, then the UK would have a moral case to say then why the fuck should we pay all this money when you are bullying us. And vice versa.

The UK position is not strong, but the EU is still being as much a dick over this whole thing as the UK is.