I went to two public schools (moved in the middle of high school, whee!) and I have to say that it was a very good thing for me. Could I have learned faster in some subjects if I were homeschooled? Sure. The gifted, however, are going to be held back by having just one teacher. I'm sorry, but unless you and your wife are REALLY well educated, you're just not going to be able to teach AP level Physics, Psychology, English Lit., foreign language, Calculus, etc. There's just too much. I took 8 AP classes from 7 different teachers and each of them were amazing educators. I just can't picture many families anywhere in the world with parents capable of combining the skills, knowledge and experience of even just these 7.
Then, of course, are the social aspects. I suppose if you get your kid in sports, clubs, camps, churches, and as many other social aspects as possible that'll help, but day-to-day interactions are VERY important. I was cock of the walk at my first high school. When I moved to the new one, I learned some humility; there were about 5-6 of us at the top of this (larger) class just as smart as I, some more gifted in various areas. Learning to live, day to day, with equals and betters is a worthwhile lesson. Without high school, I wouldn't have had my girlfriend, the cameraderie of my soccer teams (high school is very different from club soccer), my friends. I wouldn't have met people who I sincerely disagreed with, yet respected.
Am I against homeschooling? Nope. My dream for America is a country where every person gets the very best education possible in every way. However that happens, I'm thrilled when it does. I just think that there are probably some important lessons a child learns in public schooling that he just can't get anywhere else.