By taking the other OP's question into its logical extension you have (maybe unknowingly) used the specific real-world example of another question to illustrate your own more general question, @Vylix, which is
How to handle someone's getting angry over things I have no obligation to? (...) I'm merely interested in dealing with people demanding what I have no obligation to give.
This is conceptually problematic for members trying to formulate an answer, because you asked the question but the example quoted (which is not your 'actual interpersonal problem' for this question) belongs more or less specifically to SQB's case. However your good intentions are clear and much appreciated, so I shall ignore the example entirely and answer your general question with this more general answer:
Even when you are technically not obligated to do something in a particular interpersonal situation, the other person's response (getting angry, here) is influenced by his/her personal expectations which in turn have a strong social or cultural conditioning.
Since no man is an island and this person is presumably close to you, with substantial ties of blood, kinship or friendship, you need to be tactful while trying to convince them of your point of view which clashes with theirs', but also need to decide whether it might be better to purchase peace through compromise in order to maintain socially significant and potentially valuable relationships.
Frank and honest discussion with the person would usually clear up misunderstandings, but there are many issues where one brother-in-law and the other or one friend and the other will stick to diametrically opposite opinions of what constitutes obligation. In such situations you can win an argument and lose a friend, which is a useless deal IMHO.
So this is what I suggest: if the person remains angry and unconvinced despite your best efforts to make them understand that you were not obligated to do 'the thing they expected', then you should
(1) do what they want you to do, if it is not financially or otherwise damaging for you, in order to purchase peace and salvage the relationship;
(2)if it cannot be done, make it clear that you cannot do it right now, stating genuine and pressing reasons, but offer to 'make it up' in other ways later;
(3) Or else you can take the extreme step of antagonizing the person and dealing with all the social and personal problems arising from that decision.
Two pertinent examples from India:
(1) India has the 'co-brother' kinship term for the special relationship of mutual support and dependence between men who are sons-in-law of the same father-in-law: there is a strong social and cultural expectation that co-brothers will substantially help each other in need, even if they are not responsible for the situation, so much so that it becomes an ethically binding family obligation, not legally enforceable but sanctified by tradition.
In these circumstances, a person will help his co-brother in need even when it is very difficult or even financially ruinous for him to do so, purely to avoid the co-brother's 'justified anger' and also the widespread social stigma attached to 'not fulfilling his expected obligation.'
(2) Similarly an Indian man in many communities is also expected to unconditionally help his brother-in-law who is his sister's husband, 'in the interests of the sister's happiness,' but in an apparent paradox which is really a strong reflection of social patriarchy, the sister's husband does not have nearly the same burden of obligation to help his wife's brother.
