But in February, by which time the house was already partially constructed, the Board of Adjustment voted, three to two, that there had been “no rational basis” for the Historic Development Commission approving the house, and Cherry and Gordon no longer had a building permit. It was suddenly illegal for them to so much as hammer another nail, and the possibility that the half-finished house would have to be torn down became real. Just the other day they got a judge to give them permission to resume construction just long enough to close up the incomplete house and protect it from the weather, but the situation remains unresolved, and Cherry and Gordon have already spent so much money on lawyers that some local architecture buffs have started a defense fund.

Putting aside the absurdity of revoking a building permit that was legally given, months after a building is already well under way—and the requirement that its owner needs to spend money to fight to hold onto his permit—the Cherry case says a great deal about taste, not to mention different notions of what a historic district actually is, or should be. Gail Wiesner also lives in a fairly new house, built in 2008, but hers was designed to look like a much older house. Some of the other recent houses in Oakwood are also what you could call faux-traditional, like hers, and it is clear that at least some of the residents of Oakwood envision the neighborhood as a kind of stage set, an idealized little village in which every house looks like it has been there for a long time, a place where the buildings are old and only the people, the cars, and the kitchen appliances are young.

It’s not a view that prevailed in Oakwood 75 or 100 or 150 years ago, which are the very golden eras that these people want to evoke. What I found most striking about Oakwood when I visited it, along with Louis Cherry, earlier this month, is the mix of houses it contains, from stolid 19th-century brick boxes to ornate Victorians to early 20th-century Arts and Crafts bungalows. There was never, then, an insistence on using architecture as a vehicle with which to play pretend and to maintain some bizarre notion of stylistic purity. In Oakwood, the eclectic mix of styles has given the neighborhood a resonance. It shows that time was visible, and from the look of most of those old houses, the residents were proud of that fact. They knew that labels are not how you determine whether or not something fits.

What troubles Cherry most is how difficult it is to convince people that architecture is more than a matter of styles. “For most people, the idea of compatibility is ‘looks like,’” he told me. “They consider what I’m doing an affront to history. But I’m trying to celebrate vitality, and it is sympathetic to the spirit of the neighborhood.” It’s hard to imagine how Cherry could have designed a house that fit in better than the one that now stands half-finished on Euclid Street, unless he were prepared to throw in the towel and produce a make-believe Victorian. Not long ago, someone sympathetic to the plight of the house—Cherry says he doesn’t know who—started a Twitter account, @ModernOakwood, that pretends to speak in the voice of the house, with tweets like “‘Not in my front yard,’ said the house across the street to me this week. Still sad about that.”

It’s especially odd that this is happening here, since there is a lot of history for modern architecture in North Carolina, which actually has more significant modern houses than any state except California and New York. The state also has a wonderful preservation organization called North Carolina Modernist Houses that focuses on educating the public about modern design and saving endangered houses. The organizers have taken up the Oakwood cause—the first time, I suspect, that they have ever had to fight to preserve a modern house before it was even finished.

Correction: The original version of this article reported that the Board of Adjustment ordered that the house be torn down; though still a possible outcome, the Board has not specifically ordered the house razed.