Here is what causes me to be convicted of that. Perhaps you will agree and have the same conviction for your family but perhaps it will cause you to go in a different direction. I understand that. My prayer is simply that you will seek God's will in the way you raise your children.
The Bible tells us various places that Children need to obey their parents and that we as parents are responsible for training and discipline their children. Here are some verses on that:
"Children obey your parents in the Lord, for this is right. Honor your Father and Mother (which is the first commandment with a promise), so that it may be well with you, and that you may live long on the earth. Fathers, do not provoke your children to anger, but bring them up in the discipline and instruction of the Lord." Ephesians 6:1-4
"Train up a child in the way he should go, Even when he is old he will not depart from it." Proverbs 22:6
"You shall love the Lord your God with all your heart and with all your soul and with all your might. These words which I am commanding you today, shall be on your heart. You shall teach them diligently to your sons and shall talk of them when you sit in your house and when you walk be the way and when you lie down and when you rise up." Deut. 6:5-7
The reason that this causes me to homeschool is that we have more time to work on these things. If me children were to go off to public school they would be gone for the majority of their waking hours and definitely their most alert hours. Our time to train and instruct them would be quite limited. Also These verses speak of training them in the ways of the Lord - this is something that the public school teaches the opposite off much of the time and so I don't want to have to re-teach and re-train my children after they have been taught in-correctly.
Another reason I am strongly convicted to homeschool my children is because I want them to Love God and know Truth first of all. This is not what the public school teaches.
Psalm 119:160 says: "The sum of Your word is truth, and every one of Your righteous ordinances is everlasting."
God's word is where truth is found and the Bible is allowed to be taught out of in public schools so our children would not be able to study God's truth while they are in school. I want the Bible to be a large part of my children's life and their studies and so I homeschool them so that can happen.
There are many other Biblical principles that also guide me in making that decision but I will leave it at this for now.
What verses have you found that guide you as you raise your children and make decisions about their upbringing?