We homeschool our kids for pretty much all the reasons you mentioned. But if you don't really want to go into detail about the reasons you homeschool, you could just pick the one reason that feels the strongest to you, or your favorite one, or the one that you feel like would make the most sense to the person you are talking to. For example, I've met a few moms this year who used to be public school teachers and are now teaching their own kids at home. For a lot of them, they are doing it because the schools here in California are completely overcrowded. Children learn more with one-on-one instruction rather than being in a classroom with 30 other kids.
Personally, I want my kids to keep their love of learning for as long as possible, and I love being the one who is there with them when they are learning. When I see them writing in their journals, or coming up with elaborate and imaginative games and stories during their free time, or creating art projects from their own imaginations, or playing with other kids at the park, I am really happy and feel lucky that I am able to be there with them and watch it happen.
But many people don't agree with it and for some reason are adamantly against homeschooling (especially those who don't know much about it); so it's much easier to keep it simple rather than engaging in a debate. Just say that you feel it's the best decision for your family (after all, it is a personal decision for every family) and leave it at that. Or that you believe that she learns more at home. Yea for homeschooling! :-)