I know your questions are sincere, but be prepared, the socialization thing is a question that Homeschoolers hear so much they sometimes get tired of it, and can often give more of an answer then you may be prepared for!
Anyway, why do we homeschool? Lots of reasons, but primarily because we believe it to be the best thing for our children. We've been doing it for 12 years now, and our oldest(15) is starting college this year, so we did something right.
The short answer is this: Public school tends, perforce, to teach to the middle, if you're too far on either end of the curve you get left behind, and we did not want that for our kids. Plus, as a social worker for the state, I saw the kinds of discipline problems that PS kids are exposed to daily, and just didn't want it for my kids.
When our oldest was ready for 1st grade, we went into the public shool to meet his teacher, and asked her what he would be learning that year. She told us letters and numbers. When we told her that he already knew how to read, and do addition and subtraction, she said he would be learning his letters and numbers, and if he already knew them, he could help other kids. We saw no reason to set him back a year or more to conform to the average kid his age, plus We knew he would be bored to tears, and a discipline problem, so we kept him home and have never regretted it. (OK, there were a few days that we regretted it, but my wife mostly had to deal so...

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Other reasons have to do with the political correctness that rules public school curriculum, where actual facts are second to agenda's being pushed by certain groups.. (I'll leave it at that, or I'll end up on my soap-box and no one wants that!

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As for socialization, it depends on what you mean. Homeschool doesn't mean you lock your kids in the atic untill they are 18. Our kids are in lots of groups, church, homeschool groups, community sports teams, gymnastics, music lessons at the conservatory... The list is long. We spend as much time, or more, carting them from place to place as most parents. They all have a normal sized circle of friends that they interact with, we just had more control over who those kids are then we otherwise would have.
The other argument I often use is this.. as an adult, how many kids from grade school are you still close too? High School? Probably very few. How close are you to your family as an adult? I think kids learning that thier family is thier primary social group, not a random group of kids at school, is a good thing.
What our kids don't do is spend thier days in a room with 20+ other kids thier own age with one adult. Not all socialization is good! They don't want to dress like Britany Spears, or know what overpriced sneakers they 'must have', or feel the same peer pressure to conform to societies crumbling standards that other kids do.. (look out, here comes that soap-box again..

) In that regard they are hopelessly unsocialized, and and we're quite proud of that.
Studies of homeschooled kid consistently show that they are
better socialized than PS kids in ways that count, such as having the ability to interact with a wide range of age groups, not just kids exactly thier own ages, which is, by the way, a very unnatural environment, where else in life do you get it?
Anyway, there are as many reasons to homeschool as there are people who homeschool, so you'll probably get lots of answers. I for one don't think it's right for every family, or every child, its' just right for ours.
OK, now the real reason we homeschool.....
Disney in September

Just kidding, but it is nice!
Sorry if this was more answer than you were looking for, but we get this question a lot!