1) Basically the children who are able to receive an education will wind up getting better jobs because they'll have better training. Also, there won't be as many people relying on government help (such as welfare, food stamps, WIC, medicaid, etc.)
Arguments for that can be if children are able to access education they will be more educated individuals providing for themselves. The amount of people who rely on the government resources will decrease because they will have better jobs. That help can go to America's other financial problems such as research in the healthcare field. Also, it can become a vicious cycle that an adult in poverty and lack of education will not be able to help their own children succeed and it will just continue through generations. You could also make a point that educated people are more resourceful. And you could conclude that ultimately the government would be making a more profitable investment because of all these benefits.
Parents having to take responsibility to pay will cause them to be reluctant to do it, especially if they are unable to afford it. That makes it a risk that when the kids come at age, they will drop out; which in turn we are increasing the lack of education in this country and increasing the poverty level.
2) This one is saying that Education is more successful when parents take responsibility and pay for their own children's education.
The only arguments I could think of for this point is that when parents are made to pay for the students' education, that government money can go toward other country's necessities and organizations (such as the healthcare point I mentioned before). Also, it will provide more resources in the schools such as books, computers, etc. With more resources, higher quality of education can be provided. It will give educators a much deserving increase in salary.