There is a cognitive dissonance about public schools. Everyone knows public schools in the US are terrible, but everyone thinks their school is the exception. The reality is that your school would be the exception only if it teaches using project-based learning. Which it doesn’t. The public schools that are exceptional are exceptional at teaching to the test – a process that’s widely discredited. Give your kids more credit than that. Reformers say child-driven learning and project-based learning are best. Parents are the only educators in a position to do that. So all kids will get a better education at home.
When you choose something, do you like to have a wide variety to choose from, whether it is for your furniture, food, music, etc.? If so, then you could easily instill these same preferences and choices into your homeschooling style. Offer your child the best of all the worlds – eclectic homeschooling.
Without a degree, are you qualified to teach your own children at home? Rather than attempting to be an authority on everything, homeschooling parents are the bridge that connects their children with people, resources, and tools to help them reach their goals.
It must be clear at the outset that there are no sure-fire rules of education that apply to all children at all times. Reishis Chachmah quotes a Midrash that it is easier to raise a legion of olive trees in the Galilee, where the soil and climate are not conducive to growing olive trees, than to raise one child in the Land of Israel, even though Israel is conducive to proper education, since the atmosphere itself helps to imbue one with wisdom and holiness. Children are not objects to be fashioned at will, but rather human beings who have their own free will and can reject, if they so choose, even the best education. The most a parent can hope to achieve, as Chiddushei HaRim points out regarding all learning, is to put the words of Torah on the heart of the child so that when the heart opens up, the Torah found on it will sink into the receptive heart.