Depends on the situation, but schools act in loco parentis, assuming the responsibility of the parent while the child is in their custody.

The legal argument, which has been upheld by courts, is that parents don't have to respect 1st amendment rights regarding the discipline of their children, so therefore schools don't either.

And it makes sense if you think about it. A kid shouldn't be able to disrupt class, sling racial slurs, verbally assault another student or teacher, etc. with impunity. The situation in the article is a prime example of this.

I also found out the hard way that they don't have to respect your 5th and 6th amendment rights either, as I was questioned without being read my rights, and that was used against me in court.