The short answer is the ability to tailor the entire learning experience to one child's specific needs and interests. For example: My sister loves cooking so for history and chemistry she got to do it from a culinary perspective.

Extra curricular activities can help supplement public education but kids still need unstructured play time, so there is a limit to how much can be added.

I know two people who thrived in a homeschooling environment, for them it was 100% the right choice. 99% of the time it is the wrong choice.

Side note: Virtual learning has created a weird third option that isn't quite public school but also isn't homeschooling. This gets mixed in with homeschooling conversations but I think it confuses things and belongs in a separate category.