Some of the reasons we homeschool:
Freedom and flexibility from everything from content to method to schedule. Once you have a taste of freedom, there's no going back!
Individualized Instruction - curriculum can be designed based on student's needs much more effectively. Because homeschooling also allows for much more one-on-one instruction, progress is incredibly fast.
Parents are in a much better position to advocate for their children than anyone else. No one is going to know your child or care for them more than you, the parent.
Better socialization. Homeschooling isn't about hiding out at home. Homeschoolers are constantly interacting with all age groups.