I think you have to think about frames of reference. It would be wrong, I think, to put fairness ahead of being helpful/supportive within a very particular frame of reference–for example, in terms of time, to feel like if you give one kid $3K to help with closing costs on a new house, you have to give the other kids $3k this same year or else it’s unfair. Because that would just mean most years you don’t help anyone because you can’t afford to help everyone. There’s also category–just because you help one kid with housing costs doesn’t mean you have to help every kid with housing costs, because different kids have different needs. Maybe THIS kid has a fantastic opportunity to buy a house but needs help closing the gap, but THAT kid is later in a situation that they need a new AC right away. I’d rather my parents be able to help each of us how and when we need it than be concerned that each and every instance is followed by scale-balancing.
There’s also the fact that some kids just need more. I have a sister who struggles with mental illness and addiction. Over time, I’ve no doubt she’s received far, far more help from my parents than the other 5 of us kids combined. But, lord, should my parents have left her to rot in jail, let her have substandard medical care, let her lose all contact with her children, to really never even have a chance at not-miserable because they could not have afforded to provide that much support to the rest of us, none of whom had similar need? I cannot imagine begrudging her that. She’s still more miserable than any of the rest of us.
However, there should be a sense over time that parents don’t arbitrarily put one kid’s happiness over the others. I have seen that, and it’s toxic. I think it’s important that parents work to avoid this impression over time, but I also think it’s important that kids make sure they are taking the long view and not focusing on any particular moment.
That said, there’s no obligation to provide for your kids. I do think there is an obligation to live up to any commitments you make, however. I’ve known more than one family where the parents offer to pay for things, the kids make arrangements, and then the money isn’t forthcoming, or dries up. So you put your kids in music lessons mom agrees to pay for and after two months she decides she can’t cover it anymore.
Related to that, I think parents ought not give more than they can readily afford. I’ve also known several families where the parents love to be generous and give their kids too much money, but then have to come back and ask for money themselves, or decide that what they called a gift was really a loan. That sort of family dynamic makes it really hard for anyone to get ahead because anytime anyone has any kind of savings, someone else needs it, and you can’t say no because they helped you back when.