Like with most things you get out of homeschooling what you put into it. It's a big sacrifice for parents, but if home life is stable, and parents are willing to heavily invest, it holds a lot of advantages. Socialization is just not an issue for homeschoolers anymore if you prioritize social interaction - there are tons of options now. If you choose to keep them home 24/7 you will have issues, but that's a choice the parent makes …it's not due to lack of opportunities.
In terms of advantages: You know your kids better than anyone else. As such, you know how they learn, when they are "getting something", when they aren't, when they need a break, when they need a push, etc. HS allows you deep visibility into how your child works - where are they gifted, where do they struggle, what do they enjoy, how do they respond to different teaching techniques, how do they handle not getting something, how do they handle getting something quickly - at a level you just can't get in a traditional model. It provides invaluable intel to you as a parent and pays dividends more broadly in your parent/child relationship. Lastly, you have the ability to customize the curriculum your child uses to ensure they get the best available and remain challenged.
With homeschooling these days you basically have three options:
1. Do it completely on your own: lots of great curriculum out there bob jones, Abeka, sunlight, Saxon math. They come with lesson plans, all the materials, digital resources…truly out of the box, ready to go. In this model you have to lean heavily on church, clubs, sports, etc for social engagement. This is the most time intensive for parents.
2. Co-op driven: co-ops offer parents some leverage so the burden of instruction and socialization isn't fully on the parent. These typically meet once a week or twice a month. something like classical conversations is a great starting point. These provide outside instruction so your child is accustom to different teaching styles, can engage with peers, and they offer a more comprehensive solution to curriculum so you aren't selecting everything for every subject, which can require a lot of time and research.
3. University model (classical): kids go 2-3 days a week, have a pretty typical school day, curriculum is carefully curated, class size is smaller, schools are typically accredited and handle all the administration (report cards, transcripts, etc). Typically student advancement is flexible in areas your child excels…eg if they are in 5th grade but excel in math they can go to 7th grade math, or 5th grade math but excel at reading, so 7th grade orthography. They also typically have relationships with colleges for dual credit and admissions. They typically offer electives and sports (eg robotics club, computer science, chemistry club, music, arts, all the typical sports). Parents do instruction on home days and supplement curriculum where they choose to. Society for classical learning (SLC) is an organization that can help you find local options.