Can I install a hardwood floor in the kitchen?
Sure. But it's a bad idea, because kitchens are wet and have people walking around in them all the time. A wood floor will scratch and wear quickly, and be exposed to conditions that can encourage warping, rot, or mold.

So ideally you want something durable and not affected by water, and probably something that's attractive, too. That pretty much leaves tile, which, incidentally enough, is why most kitchens are tiled nowadays.