The difference is that the state has the duty to care for elderly people and children, so when they are not cared for by relatives, it has to pay professionals

The difference is that the state has the duty to care for elderly people and children, so when they are not cared for by relatives, it has to pay professionals to do it. I have not decided whether or not I support a basic income, but I do think that people, who take care for elderly relatives should get paid some reasonable fraction of the costs that the state would have to pay anyway. If these elderly people do have the funds to care for themselves, I think they should be responsible to pay this fraction, before the state has to do it. With children it is a bit more complicated, because a society generally benefits if people of higher education reproduce, which generally have a higher threshold to do so because of financial incentives. Also you decide to have children, because you want to have children. You do not decide to have parents who need care.