Yes, home schooling has certain advantages unavailable in public schools. Home-schooled students have either their parents or hired tutors who are able to give them close personal attention. Children who are home schooled are able to work at their own pace instead of having to conform to the pace of instruction in a classroom. They are able to learn in a positive environment untouched by peer pressure and bullying.
Yes, there are certain advantages in home schooling that are not available for the public schools. I have taught in the public schools and home schooled my own children. In the public school, a majority of the class time is spent in discipline and not in teaching. In home schooling, my children learned as much as students in a full day at school within a three hour period each day.
Homeschooling provides some benefits to children that cannot be attained through public education, namely the ability to work at one's own pace. Students can take as much or as little time as they need to grasp a concept. Homeshooling also provides the opportunity for a more interactive approach to learning. Students are able to take a more hands-on approach to learning through more frequent field trips.
While classes that are too large are not good for children, studies also show that a teacher to student ratio that's too low is also not good, because it singles out the difficulties of that student. Moreover, home schooling can ignore the important and significant role of socialization in lifelong success at work and home.