I am a public high school teacher and I am another vote against homeschool. I see many kids whose parents have taught them K-8 and then decide they want to send them to a public high school (which I understand, if for no other reason than for the lab sciences, the advanced math courses, and AP/IB opportunities). But the kids are maladjusted and do not have age-appropriate social skills nor do they have adequate study skills. I am required by law to give accommodations to students with IEP/504 plans, but I find I often end up giving the same accommodations to the previously-homeschooled students, as well -- just so they don't fall behind. In my experience as a teacher or a mother, I have not met a student who was successfully homeschooled for a long period of time.
It's unfortunate that you've probably been exposed to the exception of homeschoolers, not the norm. I'd be amazed if you've interacted with more than 1-2 in your classroom per year. If you do interact with more, than maybe your city is a bad area for homeschooling. Just like there are a lot of bad areas for public schools, I'm sure there are some for homeschools, too.
Op, I interact with and teach homeschooled high schoolers all the time. I previously also tutored (for years) both gifted and remedial public school students. I can tell you, as a group, the homeschooled high schoolers are as socialized (and possibly better, b/c they treat each other with more openness for differences, friendliness, and less cliquishness), as motivated, and as talented as any gifted or remedial student I have ever taught. Are they perfect - nope. No student is. But I don't denigrate an entire class of student as "maladjusted" b/c I may have interacted with a few who didn't meet my expectations. If I did, I could tell you that I'd probably have to denigrate every schooling system (public, private, and homeschooled) there is.
So, don't be scared off by one bad apple story. Whatever schooling you choose, do it b/c it's best for your child and your family and know you take the decision one day at a time. Nothing is ever forever and any decision can be changed if it isn't working. Also, be aware of the enormous growth of educational opportunities and learning available on the web. From Khan Academy to Crash Course to MIT Open Courseware online to Coursera to online AP class offerings to CK-12, etc, the ability to tailor a junior high and high school education using help from those resources can be priceless.
I will mention my oldest child (not quite high school thanks to arbitrary age laws, but taking all high school level courses) is learning Japanese 1, Honors Biology (with 2 and 1/2 Hour In-Person Labs per week for 90 hours of just lab time planned this year - way beats my high school experience for lab work), Geometry, 20th Century Fantasy Literature, World Geography, Personal Finance, and American Parliamentary Debate this year. I am using a former public school teacher, a certified biologist, a published paid author, Khan/Crash Course/MIT Online, textbooks, video courses, Netflix, and myself to provide the education for my child. She has 4 group classroom experiences (all paid by me - that's the one sucky thing for homeschooling), 1 1-on-1 tutoring experience with extra at home learning, and the rest at home with me. Nowhere in the homeschool manual does it say you have to teach everything yourself sitting at a dining room table for their whole 13 years. Instead, you can provide the best experience in the interests they have. For example, I never would have been able to get her a Japanese class in my local public school, but it's the language she really wants to learn. And now, she'll be getting ready to take her level 5 proficiency test this year. Homeschooling gives you the ability to explore their interests at the levels they are at in the way that you want and works for them. That is priceless.