Pros: your kid may fare better with homeschooling because (may, not will)
1. Public school classes can only go as fast as the slowest kid. Not so at home. Your kid won't be bored because things aren't moving fast enough to keep their interest. Engagement = better learning
2. You don't have to put up with your kid struggling with the latest bureaucratic nonsense du juor handed down from on high for the education system. You can customize how you teach to your kid's particular mental processes to maximize uptake and understanding.
3. Because of #2 you have some extra room for teaching things that the school system doesn't have time, money, room, teachers, or interest in teaching.
Cons: your kid (and you) may fare worse with homeschooling because
1. Teaching is not a job, it is a personality type. Like "artist" or "engineer". If you are not a teacher you will find homeshooling a miserable experience. Your kid probably doesn't think like you and you don't understand each other's thought processes so explaining new concepts in a way they understand is an exercise in frustration. That's what teachers are good at - figuring out what the mind in front of them needs and adapting to it. If you aren't a teacher, it won't work.
2. While being a teacher isn't just a job, teaching is. A full time job. Don't kid yourself. If you homeschool you are committing to a full time job in your own home for no pay. If you intend to do it right, that is.
3. Homeshcooling requires commitment and fortitude on your part. You cannot half-ass it and expect a good outcome. You are talking about twelve freakin years of near-daily hard work for a kid that won't appreciate how hard it is on you. It will test your patience, stamina, creativity, sanity, and resolve. Be warned.
Could go either way:
1. No schedule. There's a lot of freedom in that. But then there is also a lot of freedom in knowing all your hellions will be out of your hair six hours a day for most of the week if they go to public/private school.
2. State requirements. Some are pretty onerous. It can get expensive. Some are so lax it's ridiculous and its easy to get complacent and slack off your teaching duties.
3. Higher education. Acceptance of homeschool education in universities is all over the map. Some are favorable, some are out-right hostile. Choosing a post-secondary path is a nightmare to try to negotiate at this point, but there's good stuff out there and its getting better. So, you know. There's that.