Our family weighed a lot of options when deciding how to educate our children. Here are some of the pros and cons we found.
Home schooling advantages: Education can proceed at each child's pace, faster or slower as they need. The curriculum can be customized to each child's interest. You can include as much religious education as you want.
Home schooling disadvantages: The parents need to be experts in a variety of subjects, and be able to teach a variety of subjects. (Can you and your spouse teach high school chemistry? foreign languages? calculus? your child's chosen orchestra instrument?) Children get limited exposure to groups of children of diverse backgrounds. Education places significant time demands on the parents; it may be difficult for the parents to have full-time jobs and still home school.
Private Christian school advantages: Includes religious education in the curriculum. Includes teachers who are experts in their various subjects. Children get to spend time around groups of other children.
Private Christian school disadvantage: Costs money.
Private Christian school caution: Make sure that the curriculum is academically rigorous. Make sure that the school isn't teaching religious beliefs you disagree with.
Public school advantages: Includes teachers who are experts in their various subjects. Children get to spend time around groups of other children, including children of diverse backgrounds. Free.
Public school disadvantages: Does not include religious education in the curriculum.
Which option you choose depends somewhat on the quality of the public and private schools around you. All can be good choices, depending on many specific considerations. My children went to public school, I went to a private Christian school, and my daughter-in-law was home schooled; all proved to be good experiences overall, with a few drawbacks in each case. And in general, I prefer schools because it's better for socialization. And you know, after school, there is a university, and a kid has to be prepared for it because it may be hard to be a student after years of homeschooling. I have no homeschooling experience, but still, for me, it can be hard to focus on my studies because of different reasons. But you're always surrounded by other students who can help you somehow. For example, when I was struggling with writing a paper on Hidden Figures, it was my groupmate helped me out. She recommended me this page
https://eduzaurus.com/free-essay-samples/hidden-figures/ where I found a lot of useful examples, and then we went to the library to work on the task together. And it was much easier. And when you study at home, you miss such opportunities, and sometimes you can even give up. So that I'm for "formal' educational options, but it's just my personal opinion and experience.