I was homeschooled from 5th grade on.
The reasons people have for homeschooling their kids varies widely, from hyper-religious to anti-establishmentism to the-schools-here-suck. The types of kids people have also vary widely. So my experience is not necessarily reflective of what your kids' experience might be. That said, here's my story:

My options were home schooling or a Christian school affiliated with my parents' church. I chose to be home schooled. My mother is high school educated, not a teacher, and frankly weak on most subjects. But she loves to dig in and research options, so she did a reasonable job of finding curriculums for standard things like math. I always had a strong thirst for knowledge of certain subjects, so she left me to my own devices on those things (this was pre-internet so I think this was an especially bad strategy. How's a kid with no money going to find the best resources to learn about these things that would normally be classes?).
In general, I have always loved learning, so I was relatively easy to homeschool. By 8th grade I was scoring at the 12th grade level, 99th percentile on the CAT across the board.
I had more free time than my peers and more flexibility in my schedule. Field trips were a breeze. By high school I was taking community college classes and tutoring the adults, which was extremely helpful to have those credits when I went to college - I got to skip some intro courses and had the flexibility to take a year off of school when financial hardship hit.

So far it sounds great, but I would not really recommend it. If you don't have access to quality schools for your kid, you should move if you can afford it at all. There were a few major issues:
- Social isolation. I had little access to kids my own age, mostly my parents' friends' kids, who were, frankly, shitheads. (Not that the Christian school was better. All but one girl in what would have been my class graduated pregnant or with a child, and therefore married or engaged to be, shotgun style)
- College Admissions. I was enrolled in an online high school program at an accredited school (the first one!), but even with the transcript + 4.0 GPA in a year's worth of community college credits, colleges were deeply skeptical about homeschooling and made me jump through extra hoops. I'm fairly certain my top choice rejected me because of this.
- Misinformation & bias. I know this is an issue in school too, and my alternative option of a religious school would not have been much better, but I had to unlearn so so much of what I was taught
- Extracurriculars. Opportunities to participate in extracurricular activities are extremely limited. Many things are associated with a school and not open to non-students.

It's also worth noting that while I did relatively well in this setup, I have siblings who were also home schooled and never finished high school or got their GED.

If you do go down this path:
- Have a strategy for how to socialize your kids beyond "well, some of my friends have kids"
- Find good curriculum
- Have a strategy ready for when a kid does not want to learn something
- Make sure you or your spouse will have a lot of free time to supervise
- Enroll them in a program that will get them a HS transcript from an accredited school.
- Find ways to expose them to extracurricular activities of their choosing, beyond your own interests.