Given the choice, David Velleman would prefer to remain a closet heterosexual. By this he means that he would prefer a society in which everyone's sexual identity is regarded as entirely private:
Here are two ways of thinking about gay rights. According to the first, people can be categorized according to their sexual orientation, and members of each category should be protected against discrimination and harrassment from members of the others. According to the second way of thinking, a person's sexual feelings and behavior are private matters, which may not be taken into account by employers, schools, proprietors of public accommodations, or agents of the government, and which common courtesy requires even friends and acquaintances to leave unacknowledged in public.
Velleman argues convincingly that a sharp division between public and private life is liberating and humanizing. Yet it would be difficult to imagine what society would look like if all manifestations of sexuality and gender identity were banished from the public square. I agree that everyone has the right to as much privacy about their sexual orientation as they like. However, it's almost impossible to live a normal life without disclosing a lot of information about one's sexual orientation.
Heterosexuals simply take the public aspects of courtship, marriage, and family life for granted--asking someone out on a date, introducing a companion as your boyfriend or girlfriend, having a wedding, wearing a wedding ring, putting up family pictures at work...
I think Velleman arguements for privacy conflate sexual activity and sexual identity. He argues that privacy is desirable because shields people from mutual scrutiny without shame, furtiveness, or deciet. The norms of privacy give everyone a bubble zone in which nobody else's opinion matters. These are powerful arguments for personal privacy in general and they suggest standards against which our current social norms can be evaluated.
However, these are arguments for discretion regarding the nitty gritty details of one's sexual and emotional history, not the broad strokes that define who a person is and how they live. There's a big difference between broadcasting the intimate details of one's sex life and being open about one's overall way of life. Our society probably has an unreasonably narrow and essentialist concept of sexual orientation and no doubt too much effort is wasted trying to assign labels. However, inequality fuels these preoccupations. If every sexual orientation has the same rights, privileges, and opportunities, there's much less incentive to loudly assert your membership in the privileged group or to scrutinize other people's "credentials."