For my parents and many of their friends the primary motivation was along this line of thinking. I'm not saying this is a totally fair or accurate line of thought but it is the line of thinking that leads one to decide to homeschool.
I can take my child's education into my own hands and probably make a few mistakes along the way but at least I care deeply about my child and have a trusting relationship with my child. Children are resilant and the real things a child should learn through K-12 has more to do with character, the ability to learn, follow-through, complete a problem, read for comprehension, etc... Things that don't require a degree or certificate to effectively teach.
Alternatively, I can trust their education to the State, to underfunded schools, to teachers (some of whom are great but some of whom are in place purely because of a broken system) who may care a little bit but have to split their care and attention between 20-80 other kids none of whom are their own, to an educational system which has long been optimized in the wrong directions and for the wrong reasons.
Personally, I don't think that public school is worthless, I just think there are plenty of benefits to homeschooling that are well worth considering. Even just removing the in-effeciencies that have to exist in a system like public school, frees up so much time and energy for self-exploration, additional time to focus on things like music and technology which are underemphasized in a school "system". Additionally, if the parents do a good job of exposing their kids to an appropriate amount of socialization it removes some of the distraction of the constant social element in a school system. AKA, it's easier to focus on learning when you aren't distracted by the bully sitting behind you or the cute girl across from you. For me, I just hung out with the bully and cute girl after I was done learning.
I do think some mix of learning with social is good but there are plenty of ways to do that, again in more ideal ratios.