What drove us, initially, to homeschooling was academic concerns (contrary to the
Homeschoolers Are a Bunch of Fundies stereotype). If you listen to realtors, every school district is above average or excellent. The reality we understood is that even in an otherwise excellent school, one bad teacher can mess up the education experience, even long-term, for a whole classroom(s) of students.
The realization that schools had become anti-Christian, anti-parent, and were manipulating students toward amorality (wasting time in which they should have been teaching academics) came later. This was almost 40 years ago, and very obviously PSs have gotten far worse.
However, second most important (and quickly most important) to us was the prospect of homeschooling making our family stronger, and the extreme flexibility available in homeschooling. Some homeschooling parents school-at-home, recreate school classrooms and replicate classroom school schedules and methods. Some homeschooling parents kind of turn their kids loose to pursue their interests, knowing that pursuing those interests will "force" the kids to learn to read, do math, learn Science, and learn History (sometimes called "unschooling"). We were closer to the latter. All of our munchkins have done reasonably well, academically, and the specifics of their career fields entail the interests they pursued, to a great extent, by their choices.
"Socialization"
... sigh. Like parents are hyenas, unsuitable or toxic for teaching basic social behavior? Beyond the home, social activities depend on what is available locally. As to PSs, can anyone, with a straight face, claim that they are largely and increasingly toxic? Rural people have different activities available than big city people. Where 4-H, hunt clubs, and such are more easily available to rural people, while team sports leagues, bands, and choirs are more easily available to city people. Our experience, in the heart of Silicon Valley, was that we had to pick and choose activities so our kids had "classroom" time and weren't out of the house every day. Of course, churches and groups such as Scouts and Trail Life are readily available.