Is it against the law for children not going to school?

Yes, if you are of school age. The age varies from state to state, but most require you to be at least 16 and have parental permission before you can drop out.

The Supreme Court of the US has for the most part enforced the laws throughout the US. There have been specific rulings regarding the state laws and some adjustments have been required. One ruling allowed parents to select the education a child receives and lets them send their children to private schools or even home school them. The other is that these alternative education providers can be made to meet the same requirements as other state schools, the law applies to all education institutes.

And despite what many children would say, the law does not conflict with the 13th Amendment that banned Slavery and Involuntary Servitude.