I have to admit, there are some benefits to homeschooling in high school. The ability to work at your own pace. The ability to study what you want, when you want to.
There are also big downsides.
You don't meet people. Many of my junior high and high school friends are still great friends, ten years later. I was roommates with one for four years of college, and roommates with others for one or two years. We're spread out now, my five best buddies from high school and I living in five different states, but I still consider them good friends. Had I been homeschooled, my pool for potential friends would've been much smaller. And I don't even want to think about my social skills--let's just say I was an awkward teenager, and my friends helped me overcome that. Being homeschooled would've been a huge disadvantage there.
I had teachers in public schools that challenged me in ways my parents never could. One of them, Ms. Boburg, passed away this last week. I would not have met a personality like her elsewhere at that age. Smart, demanding, funny, sarcastic. In fact, I had a number of unique, talented teachers. Great people, great teachers, but totally unlike other adults I knew from family and church. Public schools taught me to appreciate diversity of thought, something that homeschooling, no matter how well-intentioned my parents, never could. My parents challenged me, but Boburg and other teachers challenged me in ways that my parents didn't.
I'm glad my parents weren't the ones to teach me high school biology (trust me, as intelligent as they are, I'm glad someone with a biology degree did that). I still shudder to think about two cousins of mine, homeschooled in biology with the help of a pseudo-science textbook from Bob Jones University. I'm glad I had a science teacher, a British man raised in South Africa, a BYU graduate, and an LDS bishop, who told me he accepted evolution--it made the transition to a biology major at BYU that much easier. My parents still believe evolution and the gospel are incompatible. Had I been homeschooled and majored in Biology somewhere other than BYU, who knows what would have happened. I may have, as Henry Eyring put it, seen the evidence for evolution and "thrown the baby out with the bath."
Six years of English allowed me to get perspectives on literature from six different people, who understood books much better than my mother. Even had my mother excelled at all areas of knowledge, she had only one perspective to offer, which was her own.
Do public schools have issues? Certainly. But a smart parent will put their child in a good school, ensure the child has good, demanding teachers, and encourage the child to take honors classes (where most of the good teachers teach anyway).
Meanwhile, RIP Ms. Boburg. You excelled at a demanding, poor-paying job, where you never got the respect you earned. And by doing so, you blessed thousands of lives. You are missed.