Help me understand this...you're not saying someone with Alzheimers Disease is less of a person than you or I, are you? After all, their cognitive ability is far inferior to ours.
Exactly. While this may not sit well in Happy Land, this has always been true. Our society and our legal system (and for that matter essentially all such systems in the world) hold the cognitively impaired to be less of a person than someone who is not. Most legal systems have almost always granted "lesser person" status to all sorts of humans with a wide-range of problems. A person with severe Alzheimers is not generally recognized to be as much of a "person" as you may be by legal or social convention. Same with the mentally retarded. It isn't nice, but neither is the world.
We are all animals, but it is our minds that make us "people". In a similar vein, I consider my life to have infinite value, but I am honest enough to know that my own and every other life has a very finite value in reality. These are brutal truths, and not likely to sit well with idealists. Nonetheless, I would rather see the world like it is in all its ugliness than to pretend reality is something that it is not.