I have HUGE problems with compulsory education, where in the far past likely would not - when education was solely academic. It is not anymore. Here are the problems I have:
1. Liability to parents and children. At any time, the school can become law enforcement in the most extreme degree. A 10 year old child bites into a piece of bread the wrong way and the child is taken off in handcuffs because it looks like a gun and CPS is at the parent's house.
Some schools have become so radically liberal and so intensely hateful of such as the military, that any kid playing cops and robbers is treated as a terrorist and this put into the child's permanent record.
2. Political correctness. Political correctness has become the primary goal of many school districts. It is far more important that the children are taught to hate religion, love Obama, accept homosexuality as fine, etc etc - regardless of and despite of parents.
3. Teaching children to despise their parents. For many schools, if the parents are religious, conservative etc, the children will be required to be tested and give answers essentially declaring their parents are ignorant bigots to be despised.
4. Standardized tests. You child can be Einstein in mathematics or Stephen King in writing or one of the greatest of all artists, but lacking in another area will essentially obliterate a child's academic future.
5. Using schools to gain information on parents. Children are not given Miranda. Nor are parents even notified if a child is going to be questions. Little children can answer questions in ways they are suggested to answer.
6. Danger to the children. Most schools essentially advertise that all the children are unprotected and that would be a criminal offense for anyone to be able to be in a position to protect them. Requiring children be taken from the safety of their homes and put into an open and advertised free and unstoppable shooting gallery is not something any parent should be required to have their children essentially seized by the government for.
7. Shocking as it may be, some parents don't want their 13 year old given condoms and explained about "safe sex," when many (if not most) parents don't believe there is such a thing as a 13 year old having "safe" sex - neither psychologically or health-wise, and telling a 13 year old there is such a thing and giving tools to have it is, to them, is as corrupting and dangerous to their child as is possible.
In short, it no longer is just compulsory education. It is compulsory social, moral, ideological, political and both forced and tested indoctrination by any wackjob teacher or administrator, and in ways that can cause real and lifelong damage to the child's formal record - and that of the parents too.
I do not agree with the reasoning of the OP directly in that society and for the sake of the child an EDUCATION should be required. However, compulsory education to a specific school the government specifically requires should not be - because schools just aren't about education anymore. They are about indoctrination and they are about taking risks with your children's minds, morals and physical safety - which can be diametrically opposite and requiring students to express contempt of their parent(s) morals, values and home education.