A Christian would likely choose Christian education because it helps strengthen the faith "triangle." The three parts of that triangle are church, home, and school. A family can effectively teach a child from a Christian perspective at home. That teaching might include Bible stories, basic tenets of faith, and behavior from a Christian perspective. Going to church will further deepen and bolster a child's faith education. He or she will be a part of the larger Christian community by attending church.
Attending a Christian school will even further integrate faith into that child's life. Church is maybe 90 minutes per week, which, if that is the only time a person spends on his or her faith every week, is not a lot of focus on faith and religion. Family time can increase that, but for at least 35-40 hours per week a child is in school, not in church or spending time with his or her Christian family. Attending a Christian school allows a child to learn the standard curriculum mandated by the state while at the same time having it taught from a Christian perspective. The faith base and standard education are woven together instead of being held separately, which public schools require.
Christian families also might choose Christian education because private, Christian education often hold students to higher standards than public schools. Consequently, test scores and college admittance rates are frequently higher for students in private, Christian schools.
Christian families also may choose Christian education because their child is more likely to be surrounded by friends and families who share the child's basic understanding of morals and behavior. This reinforces what the family teaches at home and what the church teaches on Sundays.
Churches often encourage Christian education because students educated in Christian schools are more likely to make church attendance a part of their life for their entire life. A study was done on this very concept a few years ago. It is called the Cardus Education Survey. I've attached the findings for you in the 'Sources' section below.
As for Christian education being a necessity in the modern age, I can't confidently claim it is an absolute necessity. I teach in a Christian school, and believe in all of the advantages that I wrote above. I also believe a child can receive a good education from a public school and grow up to be a strong Christian as well. If a family's goal is to teach a child that the Christian faith is all encompassing, and that faith is integral to all aspects of life and subjects, then only having the child learn about faith and God at home and in church presents the child with a lopsided Christian worldview. In that light, Christian education is necessary to educate a child about God and religion in as many aspects of his or her life as possible.