Die Eule wants to ensure we know that "chair" is Stuhl, and accepting "stool"--even though technically correct--does not help and would very likely lead people to never realize that the primary usage of Stuhl is in the sense of "chair". And when I say "primary usage", I mean at an approximate rate of about 84:1 (7,025:84 per dict.cc. See http://www.dict.cc/?s=Stuhl).
I find it interesting that no one complains "why isn't 'that is my feces' accepted?" It makes me think that most objections to "stool" not being accepted for Stuhl are from users thinking that Stuhl is one of these:
Of course, advanced users--who fully understand the difference between Hocker und Stuhl und Kot und Liege and stool and feces and chair and cot, and who also have a need to memorize phrases useful for when they don't flush or otherwise leave their poop lying about in places where ownership of it is questionable--can surely be expected to remember that DL doesn't accept this particular usage of Stuhl.
In English "that" is usually referring to something a bit further away from the person talking about it, and "this" is for something closer. It can be ambiguous, though, and there are definitely situations where you could say either.
In German, this distinction isn't so common. You could say "das" to mean either "that" or "this", so you don't need to make a choice about which word to use like you do in English. If you want to be more specific and say "this one here" or "that one over there" you definitely can, but it uses more words ("das hier" or "das [X] da drüben") or get into using dies-.
Then how do you say "stool" in German if this one is meant for only "chair"?