This is some of my reasoning in making the decision of whether or not to home school. I have very little against homeschooling. If you home school, more power to you. It's just not for me. I have considered it. I've read lots about it. But, I'm not going to right now. (I'll leave the door open for later though, because you never know what changes may appear). Here's why:
For HS: customized curriculum for your kids. If they need extra help, you can spend more time on something. If they are ahead of the game, you can speed them up so they aren't bored.
Against: When a child grows to be an adult and gets a job or becomes a parent, there are times when they will need to step up the pace and do the boring things until they are complete. I figure doing that in school is a way to help my kids "just deal with it" that sometimes life is boring. Also, as a parent, it is my job to tutor my children to help them catch up. If they are ahead, I would encourage them to do something to stretch them. Plus, our school does a "classrooms without boundaries" type of thing so that if your kid is strong/weak in something, they can go to another grade for help.
For HS: My own schedule! I hate having bus stop times! I guess I'm spoiled now.
Against: None. I love the idea of not having 7am pick ups and 3:30 drop offs.
For HS: Study whatever you want. No teacher saying "And now Kacy isn't going to read with the class because I need to hear the rest of you." and "Kacy is not going to help you with the calendar today because she already knows her numbers..." and if Kacy already knows all of this, than it would be nice if she could move on to the next subject. Basically, there is a ton of time wasted in school if you are kid who "gets it" the first or second time.
Against: I've met lots of people who don't "get it" in adulthood the first time, and require more patience. The workforce taught me that. Plus, it's good to have my kids learn to help other kids while they are young.
For HS: None of the social junk- lying, cheating, bragging, self confidence issues, most popular, skinniest, smartest, all the "-ests" you can think of. No "bad" influences.
Against: I don't want my kids to be sheltered from the real world. Just based on a life experience of mine: I went to Utah State for 18 months. It was a culture shock. Not only could I not find a decent tortilla, but I found most (please note "most". Not all. Not everyone. Just, "most." Thank-you.) of the people there to fit into three main categories: The LDS people who were very narrow minded (in that really bad way- not the "I don't believe in drinking beer, so no thank-you", but the "I can't believe ANYONE would even drink a beer. They are bad people."), the LDS people who were very rebellious, and then the non-LDS people just trying to survive a dominant culture that could easily present itself as "the only right way". Well, being from CA and never in a majority, this disturbed me. I think it's great my kids will be confronted with choices to make and different people to deal with. I will not hide them in my home from all the crap, rather I will teach them what we believe and why. For example: Ryan and I are traditional in the fact that we believe boys shouldn't pierce their ears. It's a girl thing. Kacy came home and said in her most scandalous voice, "Mom! There is this boy at school who has his ears pierced." I said "So?", to which she replied, "But Mom, boys aren't supposed to get their ears pierced. It's only for girls!" My reply to her went something like: "Kacy, don't you dare go tell that boy that only girls are supposed to pierce their ears.(Because she would...) He and his parents must think it is okay to do that, and it's not against the law. In our family, the boys will not pierce their ears, and if they do they will be in big, big trouble. Some families do different things. It's what YOU do that matters. Okay?" And as for self esteem issues, I think parents can help with that LOTS and LOTS.
For HS: Spending hours and hours engaged in deep philosophical conversation with your children.
Against: What? Hours and hours? And hours? Um, maybe not. :)
So basically, my academic reasons are weak. I will supplement/study with my kids anyway, after hours, on weekends, and especially during the summer. My social reasons won out. And, if you really want to refute my arguments, do. But, I'm not going to change my mind. I want my kids to be great leaders, and I will do what needs to be done to help them grow into confident, productive people of noble character. I think that they can do those things even while in public school, despite what the Internet says.