As a psychological matter, the role of upbringing is quite important in explaining why a person holds the beliefs that they do -- most people either accept, or rebelliously invert, what they were taught as children. But Pace isn't telling us that regardless of what's right he's psychologically impotent to change his beliefs. He's making an argument, trying to convince others to support him in keeping homosexuals out of the military.
But of course the appeal to upbringing is a thoroughly relativist argument. Plenty of people these days were raised to believe that homosexuality is just fine. (And others of us were brought up without any strong message either way -- my family is fairly conservative in general, but on this issue it's more passively heteronormative than actively homophobic.)
Pace has since tried to shield himself from criticism with another classic relativist argument: he says he was just talking about his "personal opinions about moral conduct."