My three boys (all teens now) have been homeschooled for at least half of their years. The one who has ONLY been homeschooled (now 13) is the MOST outgoing. I also have a more quiet son and then another more extroverted son.
My point is this: a person's innate personality is there from a very young age, before you even start homeschooling! I know all sorts of introverted kids that attend public schools- because this is their innate personality!
Having said this, I do believe boys especially need to taught when they are older as much as possible by other MEN. We have allowed our kids to take a few classes part time at a Christian school in high school. By the way, the education there is not better at all! Taking band and a foreign language has been a good fit for us though.
Remember, homeschooling is not perfect! However, I have had kids in public and private schools too and I'll still take homeschooling! Remember to think LONG TERM! They will be in college soon so don't give up!