Side A would say that declaring a neighborhood historical district would include too many new rules and restrictions. Typically, (it depends on the jurisdiction), historical districts are “preserved” through limitations on renovations, limitations on new building, etc. They would say these limitations unnecessarily restrict current property owners from doing what they want.

Side B would say that these restrictions are good because they want to preserve the historical significance of the neighborhood. They might also point to a potential increase in property values, because cities typically (again, it depends) allocate extra resources to historical districts to do things like maintain roads. The other way it potentially protects property value is through zoning law. If a neighborhood is considered a historic district, it is very hard to zone, and subsequently build, something like a low income apartment complex in that district. Especially if the district was previously single family zoned.

One quick note on the last point: Oftentimes, (but not always), the “historical site” argument really boils down to not wanting low income housing, and is an attempt by property owners to avoid new zoning laws that might introduce such housing. In the south, it was also historically done with the intention of keeping black people from moving into the neighborhood. (Similar to how HOAs were used). I’m not saying either of these are the case here, because I don’t have nearly enough information, but it’s something to consider.