I am curious during what context you have conversation with the parents of people you interview about whether or not they feel their child is socially awkward?
It may be the culture of homeschooling in NYC vs. other regions but I have to say the homeschooled kids I have met (of various ages) are super awesome and pretty much the opposite of socially awkward. It's part of the reason why we got interested in homeschooling in the first place...I say this as someone who didn't even think about homeschooling until I started meeting homeschooled kids who were almost UNUSUALLY well-adjusted in comparison to many of the other (traditionally schooled) kids I knew and taught.
It's actually kind of funny - and please bare with me that this is just my personal experience in my little corner of the world here - but more times then I can count I've had parents of homeschooled kids call and ask me why I didn't hire their son or daughter. Seriously. Um.. I didn't hire them because I received 100 applications and interviewed 10 and hired 1, your kid didn't make the cut for what ever reason, but it's nothing personal. 8 other kids didn't get the job either I've had parents try to fill out the applications for their kids, and even want to sit in on the interview.
We also participate in a "job shadow" program where kids can come volunteer for a few hours and get school credit and the homeschooling parents are usually really pushy and want us to make exceptions for what their student will do - what paper work they submit and how they turn it in, they hours they can participate, etc. Maybe camprunner hit it on the head - the awkward parents create the awkward kids regardless of homeschooling or not lol
I will admit that I *HAVE* known/hired some great people that were homeschooled and I have several friends that are homeschooling their kids and I'm sure they're going to turn out fine. I guess what I'm saying is that it's really easy to do a crappy job at it and really hard to do it right. Maybe there are just a lot of lazy parents in my area (I'm in the suburbs but close to some very rural areas). It's really easy to "say" public school sucks, but being a teacher is hard work so if you're going to do it yourself you have to be 110% committed to doing it right. I feel very blessed to live in an area with good schools and awesome teachers and if that weren't the case I would look at my other options too.
And just to reiterate, I mean no harm here and am merely voicing an opinion as someone who potentially has to employ and/or work with your child as an adult