It doesn't show that. Subsidies will shift the margin of who can afford to have a stay at home parent, so if being raised by a parent is better than childcare,

It doesn't show that. Subsidies will shift the margin of who can afford to have a stay at home parent, so if being raised by a parent is better than childcare, you expect people on the margin to lose out. This is in contrast to something like a child subsidy that could be used for childcare or to support a parent raising the child (e.g. in the US, increasing the refundable child tax credit).