That's a common form of homo-phobia (phobia as in fear, not as in hate). It's the attitude I see in people insecure about their own sexuality, who see a problem where there is none.
Giving it another name ("homophobia", "insecure about their own sexuality") does not make the issue go away for the people who suffer from it.
You don't magically grow more confident about your sexuality (or your whatever) by hearing that you are insecure about it. Or at least, I don't know how.
I can also relate to the awkwardness of asking someone to hang out one-on-one. It isn't necessarily borne out of sexual insecurity, but rather out of social awkwardness.
