Actually, correct.
Hatchbacks and wagons are styles of car bodies. Wagons generally have longer rooflines and more upright rear hatches, but are otherwise basically the same as hatchbacks. When the first hatchbacks came out, they were marketed to people who wanted the "utility" of a wagon. But "wagons" had gone out of style, and fastbacks were "cool", so hatchbacks were designed. CUVs are raised wagons/hatchbacks with taller bodies, but still based on car unibody platforms [whereas SUVs are body on frame].
The CX-5 is a CUV, which is a fat, taller, raised hatchback or wagon, depending on how you look at that beautiful fat bootie.
But who cares what you call it. It seems like you've got that old American antipathy to "station wagons".
I'm really glad you love your 14, CD. Don't let anybody rain on your parade. Yours was the sportiest mid-priced CUV in 14. The CX-5 still is. But it ain't now and never was a "driver's car". It is, and was, the best CUV for people who like driving, a "driver's CUV" if you must. Which is probably the ultimate reason that any of us bought ours instead of one of those other brands.