If I as a taxpayer am going to subsidize someone else's activity, then why shouldn't I get a say in how they perform that activity?

If it costs $100/child at a daycare facility, but $200/child for someone to be a stay-at-home parent, and you're asking me, a random taxpayer, to pay for one of those for someone else, from a financial perspective I will likely prefer to pay for the former.

Now, I personally don't get to decide where tax dollars go, but I could easily imagine there are enough people with this preference that it could influence public policy.

Having said that, if it's actually significantly better for a child to have a SAH parent, I might change my tune. (My mother was a SAHM, and I think that was great for us growing up.)

The ask isn’t for more for the parents who stay at home, it’s for the equal amount.

In your system you’ve created a messed up incentive where parents are better off just sending the kid to the daycare and having the mom sit at home and do absolutely nothing.