I am no longer home schooled myself, but I was home schooled up until last year for my entire life (11 grades, with a few classes at home school co-ops) so I feel that I'm qualified to share my views.
What do you feel are the benefits of homeschooling? I can't think of any meself.
1. Great flexibility for children that are not normal in their intelligence. (Either very intelligent or unintelligent)
2. Great flexibility in learning. Homeschoolers can focus your studies more towards where your interests are. (For me, that'd be history and philosophy/theology)
3. Greater control over what your child learns, if you want to exercise it. (Whether this is a plus or minus depends on your perspective, I suppose)
4. Greater time flexibility. (While homeschooled, you can take field trips whenever you want to, and if there are times when you need to stop school to do something else important - missions work, farm work, or whatever, you can do that easier than in a public school)
Basically, it's all about greater flexibility. Homeschooling isn't for everyone, but it can be a great alternative to the standard public school fare.
How many real life friends do you have?
Socialization is definitely one of the weaker points of homeschooling. However, there is almost always organizations or groups that the parents can get involved in. Whether it is NCFCA speech and debate, or a local co-op or KONOS group, or whatever. These days, there are home schoolers almost everywhere in the US. Additionally, many school districts let home schoolers take part in their local sports teams, so if there isn't a YMCA or anything similar that you can use, you can still get involved in sports.
How do you manage to motivate yourself to do work without procrastinating? I would procrastinate massively if I was in your situation and never get any work done.
The other big issue with home schooling.

This especially happens with older home schooled kids (Like I used to be) who are effectively teaching themselves, because their parents are often teaching the younger kids as well. I basically taught myself 3/4 of my first three years of high school. I believe I may have accomplished less than I would have if I'd been held more accountable, but I seem to be at least up to par with non-home schoolers. (In the private school I attended this past year, I got a 4.39 out of a 4.5 GPA grading system.) And in an odd way, perhaps my "wasting time" on the internet or reading books when I should have been doing Algebra and Biology worked out for the best - I now have a good pool of general knowledge, and I'm a fairly good debater and thinker for my age. Personally, I'd rather really learn to think for myself over memorizing the different kingdoms and phylum and all that by rote.
Some kids are really motivated, though. I had friends who finished all their textbooks months early. Really this depends on how motivated the kids are, and if they aren't too motivated, the parents need to make sure the kids are doing their work.
Thanks for the answers. Sorry to hear about brother though

I wanted to know about the requirements for homeschooling exactly because of some crazy people. Sounds a bit frightening that some fundie nutjobs can teach their children in their own home without people monitoring the standard of teaching.
This actually brings up more questions. I don't know much about the American schools systems, but do you participate in some exams for the state or something with which they can monitor what you have learned so that the university/college you might apply for in the future knows what kind of a person are you? Of course you do, right?
This varies from state to state. Some states require some sort of periodic check ups to make sure the kids are learning, and standardized tests every year. Other states may not have any regulation at all - all you have to do is send a letter to the school board notifying them of your intent to take your child out of school, and teach them yourself. (And my Mom never even did that, because we moved around every couple of years and technically weren't local residents - technically speaking, I played hooky my whole life, if you only consider the public school system)
I took standardized tests most years I was homeschooled, and I think that's the norm for most homeschoolers.