First of all, the government can't pay for bubble gum. The taxpayers pay. Willingly or otherwise.
Aside from that, there IS no difference except for one :
If you fail to accept government pregnancy "help," you will not be threatened with arrest and government harrassment.
But if you try to opt out of government schools, it is a whole other thing. Harrassment, persecution, threats, arrest and prosecution are not out of the question.
See the difference?
If you are independently wealthy, the first example is academic. As is the second, if you can afford any private school you choose; that isn't illegal --- yet; or legal representation and the time and effort legal resistance requires.
Freedom should not vary, depending on how big your savings account is.
My saving account is quite small. I am free to homeschool my children. You can legally opt out of public school. However, you make a very good point. We should do away with compulsory attendance laws.