I don't think that the author was asserting that homeschooling can lead to homosexuality, but is urging parents to ensure appropriate "play" time amongst peers. Boys have a distinct effect on each other; while they may start out playing gently, invariably, they will start crashing cars, dinosaurs will crush pretend villages and devour the villagers, and all sorts of "imaginary" mayhem will occur.
Boys need to be rowdy, just a little bit, everyday. They need a few cuts and bruises from spills and daring adventures. I've seen too many moms, in their loving efforts to protect their sons from perceived danger, verbally emasculate them.
Further, the author does qualify his support for homeschooling by pointing out that homeschooling parents tend to be more involved, more supportive, and provide more traditional gender roles than "modern" parents. I think he was just giving homeschoolers a "heads up," nothing more.
As to your comments concerning the current state of many households, I wholeheartedly agree. There are way too many children being raised in homes with just one parent. I know far too many children who have no father, absent fathers, or useless, uninvolved fathers. A shame.
As an aside, my husband can't understand why I sometimes let my son "sass" me back or pitch a fit. It's simple. My boy is a stubborn, willful child - has been since he was born. If I constantly suppress that strong spirit of his, I will break him or he will grow up hating me. I don't want him broken. I want him to love me, fear me at times, and understand that there is a BIG difference between right and wrong. I certainly don't want to be his "friend," like too many other parents do - that conveys an equal status and we are most certainly not equal. But I want him to feel comfortable enough in our relationship to bring his problems to me, which is why - at times - I don't always pounce on things, particularly minor things. I want him to know there are times when I can see his side, too.
Being a parent is the toughest job in the world. I can only hope I'm doing half the job raising my babies as my parents did raising me. Thankfully, my husband is unmistakably masculine - in his looks, body type, conduct, and manners. He is very close to my son, and I am struck anew, daily, at how my son emulates him - even down to his swaggering walk. I'll have to show this article to my husband, to remind him how important he is in our son's development.