This question comes up a lot... it's not a simple answer.
The immediate problem that we had at the time we made the decision to home school was that we were moving for the second time in a year and because we were only renting we knew there would be another move coming. Continuity was being disrupted once again, and we were not completely sure of when the moving would stop. The solution that home school offered was continuity. They didn't have to start over every year.
Another problem we had was class size. The girls went from being one of 22 to one of 32. As a former teacher, this bothered me. It became a real problem when I started noticing some issues with my then first grader's writing. The teacher was overwhelmed, and could not tell me or even help figure out what my daughter's struggle was. She wasn't a discipline problem and she was a good faker... so other than myself, nobody seemed to think there was anything wrong.
So these circumstances really pushed me to look at home school as an option. I had always been attracted to the idea of teaching my own children. After all, I was a teacher in my before kids life. However, I was afraid of failing my children some way. When I began researching home schooling, it became apparent that my worries were unfounded. Everyone worries about being a good enough teacher for their kids...I have an education and a background that should give me the confidence to overcome those fears. Realizing this freed me up to really look at home school and discover if it would work for our family.
There are a few specific things that we really love about home schooling. The flexibility in schedule, the opportunity to expand our children's education beyond standards set by the department of education, the teacher to student ratio, and the shared experience our kids have with us and each other are some of the biggest benefits.
The flexibility of the home school schedule is a HUGE benefit. Our current state (WA) requires 180 days of instruction, just like the public school. But we can use those 180 days at any time and in any way we want. So rainy summer days become a school day easily, instead of a wasted day watching TV. When I was pregnant with our little boy, we planned to take 4 weeks off starting mid-September for his birth (which ended up including a week long stay in the special care nursery). The girls didn't miss an hour of school for it, we just started early and used some Saturdays. We are planing a big move across the country in a few weeks. Again, we will be pushing pause on the school year for a couple of weeks (though you can bet the drive will include some educational stops along the way).
We have also enjoyed going beyond what a public school education would include. We have added Bible and character education to our curriculum. Taking the opportunity to deepen their (and mine as well) understanding of our faith. The girls are also starting Spanish lessons this year, an opportunity they would not have until later in our current school district.
Invaluable is the 1:3 teacher to student ratio of our home school. Teaching my children has given me an insight into their learning abilities and struggles that I had not been able to see from outside of the classroom. I understand now what my now 3rd grader's struggle is with reading and writing. I get to help her focus on her strength and the creativity that gets stifled in a large classroom.
The shared experience that all of the girls (1 year old boy is not yet being "schooled") have has brought them closer. In the last year of public school I noticed that the girls would fight a lot when they came home but during extended breaks they were best friends. They get along all the time now. They are each other's best friend. As a family unit, we just have more time together. We spend fewer nights struggling through home work, because it's all homework, done during the day. We go on adventures to explore something we are learning in school. We look for educational value in everyday activities (something I wish I had done more of when they were in public school).
Home schooling fits our crazy family. It works for us.