Public school does have some advantages. Free babysitting is the prime one. You are already paying for it, so why not use it?
- predatory teachers and students
- subjects that are not in line with your belief systems
- indoctrination in beliefs that promote thinking that is not in line with your values
- possible harm from abuse by teachers or other students
If you are worried about socialization of your children then get them involved in various activities where they actually learn something such as 4-H, sports, or martial arts. These activities can grow into adult hood with them while they are learning with others who are working towards a common goal.
If you must send your children to public school then take stock of what they are actually learning. Read their text books. Talk to them about their day. Visit the classroom on an unannounced schedule and listen to what the teacher is doing. Watch the other children and see how they behave.
We brought them into this world and it is up to us to see that they have the learning they deserve with out being subjected to unsavory elements.