How is a consumer supposed to know that business isn't offered on that flight? It says it's "Not Available", but that's the same as what aa.com will show if the cabin is sold out. Especially close in, I pretty frequently see three cabin flights with business sold out even though first is available, and I don't think anyone takes that as a sign that the first class cabin somehow gets downgraded.

It seems like the "Flagship" First designation is probably a bug, or AA should just be marketing the service as Business class, but I agree that the current display is pretty misleading.