You Control the Environment
The major advantage to home schooling is that you control the environment. You choose the curriculum, you choose the pace. If your child is slow to understanding a concept, you have the freedom to allow the extra time your child needs to completely understand the topic. There just isn't this level of individualism in public school. Public school is equally hard on the under achiever who feels lost when the rest of the class moves on and for the over achiever who is bored because they grasped the concept long before the rest of the class. At home you can vary the pace to give both types of students the freedom they need to succeed.
Most public schools are overcrowded with 30 or more students in a classroom. The shear level of noise and commotion with this many students in one room makes learning difficult. With home schooling, you control the noise level and can limit the number of interruptions in your child's day.
Many parents are opting for a Christian home schooling curriculum to reinforce their values and morals. Public schools cannot teach religion and may not teach the moral values that are important to you. At home, you get to decide when to discuss sex education with your child in a private setting. In public school, sex ed is often taught in phy-ed or health class in a large group setting with lots of snickering and embarrassing comments. 'One size fits all' sex ed. Are your values being taught? Probably not.
Home schooling is a great answer for parents who want a stronger math or science background for their child. Whatever it is you want your child to learn, there is curriculum available that the home school experience can provide. Many students learn best with tactile, hands on learning. Most public schools do not have the funds to provide hands on learning to children. Through home schooling programs, you can tailor your program to fit your child's style of learning.