Consider religious aspects since this is one of the key factors for many families. In public schools, there is more likelihood that the child will be exposed to non-Christian viewpoints and suggestions than at home. Other families believe that having their child in a public school as witnesses for their faith is more important, and they trust the fundamentals they are teaching at home.
Let your child's individualism come through, or not. In public schools, children are less likely to express individual viewpoints mainly due to peer pressure situations and wanting to be just like their friends. In homeschooling they are less likely to be influenced by others and therefore more able to be individuals.
Give children the ability to make friends and learn to work as part of a team. Children in public schools have the ability to socialize with a larger group of people, often helping them to improve their ability to communicate and develop relationships on their own. Homeschooling children are unable to do this, or will be restricted by those social activities their parents provide for them.
Educate your child at their pace. A benefit of homeschooling is the ability to keep your child's education at the speed that is appropriate for their needs. In a classroom, it is hard for the student to have the teacher's attention for longer than a few minutes at a time. Plus, the class works as one, leaving behind or keeping behind some students.
Compare the benefits of teaching the child yourself. While in a homeschooling atmosphere you will be able to teach how you want and what you want, you do have to teach. Many parents are unfamiliar with advanced studies and lesson plans may be difficult for the parent to use.