They pay for everyone else's children through their taxes. Money they could use elsewhere for their own needs or pleasure.
-- To be clear, I'm not saying this is necessarily a bad thing. I don't have population charts of Austria on my desk and I'm too lazy to Google it right now, I'd assume it tracks a similar trend to the rest of the Europe and it's slowing down. In that case it might be for the common good and might come back as a positive to the individual at some point in their life.
I'm just saying it's not easy to come up with a scheme that is/feels fair to everyone involved, especially if there's no justification for it. One could find justifications for child support maybe, but can you justify freeloading just as easily?
I'm pretty sure people would be a lot more hesitant to complain about others getting UBI if they get it themselves.
And last one: as UBI comes from taxes (the state generates 0 money, just collect from others), what about those who decide not to work at all? How long until some of them stats asking for an increase in UBI because they cannot get a rent in the city?
It seems you have an idealistic view about human nature and that everyone is good and honest, not greedy, etc. The reality is not bad, but not so naive.
There's a precedent why I think that people will approve of "universal" income: We have "Familienbeihilfe" in Austria. It's a payment of roughly 200€ per child that parents get. Everyone gets it, regardless of income, so noone is jealous. It's the best way of distributing financial aid in my opinion.
Regarding special needs, in my experience it's much easier to get aid for disabilities. I have a kid with special needs, and it's incredible how helpful people are. Social workers are calling us to tell us what kind of aid we should apply for and help us fill out forms etc. It's completely the opposite experience of applying for unemployment or for aid with rent payments etc.