While I wouldn't call the enrollment of a child in public school necessarily advisable (especially depending on what area the school's in--some public schools are worse than others), I wouldn't go so far as to call it sin. Sure, God wants what is best for us and our children, and more often than not, home schooling is just that. But, what if: the family's in the lower-middle class; Dad's away at work most of the day. Mom would teach but she just doesn't have confidence in her ability to do so. On top of this, she's recently been diagnosed with bipolar disorder, and it's often a fight for her just to stay sane. Complicating this even further, the oldest child has a speech impediment that requires therapy, and dad's wages are just enough to provide the essentials, make payments to student loans, and maybe enjoy the very occasional luxury.
The budget cuts here and there, even were they to be made, would not even come close to paying for the oldest's speech lessons. But just across the street, the public school is offering free speech lessons once or twice a week to needful students. Is it a sin to want to see your child have a chance at normalcy under these circumstances?