Translation:That dog is not scary.
Well, what I know is that the first hat-selling dog (https://forum.duolingo.com/comment/22992241/%E3%82%8F%E3%81%9F%E3%81%97%E3%81%AE%E7%8A%AC%E3%81%AF%E3%81%BC%E3%81%86%E3%81%97%E3%82%92%E3%81%86%E3%82%8A%E3%81%BE%E3%81%99%E3%80%82) bit a man (Der Hund beißt den Mann - https://forum.duolingo.com/comment/11197429/Der-Hund-bei%C3%9Ft-den-Mann) then it died (先週犬が亡くなりました - https://forum.duolingo.com/comment/23254698/My-dog-died-last-week). The second hat-selling dog does not bite, so is not scary. It seems that it can dance also (seen at two instances! https://forum.duolingo.com/comment/24974155/%EA%B0%9C%EA%B0%80-%EC%B6%A4%EC%B6%A5%EB%8B%88%EB%8B%A4 and https://forum.duolingo.com/comment/8843990/La-hundo-kaj-la-porko-dancas-nokte)
Because there is no such form as こわかっていません
こわい is an adjective and the negative form is こわくない or こわくありません. There ia no continuous form. It is a subjective adjective, so it can only be used to express feeling of myself i.e. the 1st person.
こわがる, on the other hand, is a verb expressing feelings of 3rd persons. It expresses "states," so 怖がっています means the subject is in a state of fear.
While KeithWong9's answer was appropriate, I think that it would be useful to study the は..が sequence. As in, 私はあの犬が怖くないです。田中さんはお寿司が好きです。 Actually, in this instance, I can see this phrase having the additional meaning that the dog is not scared (of something). その犬は（車が）怖くありません。[That dog is not scared (of cars).] A lot of it is context based, and native speakers often drop the particle, saying Osushi daisuki、inu chou kawaii, etc., but having the knowledge of when to use は and が, while extremely confusing at first, is essential to having a higher command of the language and being specific with regard to statements, thus alleviating confusion.
Got my finger on it!
If the topic of the sentence is the speaker, then you would use the は-が pattern...
BUT if the topic is not the speaker, then you should be using the は-を pattern with the ~がる conjugation on the adjective. The exception is for embedded clauses (if things like と言う or そうだ is attatched to the end of the sentence, then it does revert back to the は-が pattern).
Example sentences from "A Dictionary of Basic Japanese Grammar" by Seiichi Makino and Michio Tsutsui under the notes for ~がる to follow.
ぼくは犬が怖い。(To me, dogs are scary = I am scared of dogs)
深田さんは犬をこわがっている。(Mr. Fukada fears dogs)
深田さんは犬が怖いと言った。(Mr. Fukada says he is scared of dogs)
No, it would be sono inu ni taisuru kowagarimasen (literally - I don't have fear in regards to that dog) I'm not afraid of that dog. その 犬 に たいする 怖がりません。 The difference is that kowai is an adjective (meaning scary) which is describing the dog (the noun), and kowagaria is a noun (meaning fear). You can't possess an adjective (scary), but you can possess a noun (fear). And that is why this sentence does not mean - I am afraid of that dog.
It is the wrong English translation for this Japanese sentence. "そのいぬはこわくありません。 " This sentence is describing その いぬ the (that) dog. It is a simple this equals this type sentence - in this instance however, the descriptor (adjective) is negative so - this is not this. This sentence is not talking about the speaker or how the speaker feels about the dog - it's describing the dog, telling us that that dog is not scary. That is why your answer was incorrect.
You are welcome - however, it is not my opinion - it is a fact. Also, something I neglected to say before - in this sentence こわい is an adjective describing the dog - the dog is scary. The difference between that and your sentence is that you are using a verb - to be scared.
To be clear (again as it has been discussed before), in Japanese, any adjectives describing subjective feelings, e.g. 好き 嫌い 怖い 痛い 嬉しい etc., cannot be used to describe 3rd person's feelings. To describe 3rd person's feelings we can add ～がる to form a verb (for most of the i-adjectives) or ～そうだ/ようだ to describe objective feelings.
犬が怖い (My feeling to the dog) The dog is scary.
犬が怖がっている(The dog's feeling) The dog is scared.
目が痛い My eye hurts.
目が痛そうだ His/her eye hurts.
お寿司が好きだ(My feeling) I like sushi.
田中さんはお寿司が好きだ (It is technically wrong but I hear people say this)
田中さんはお寿司が好きなようだ (It seems that) Tanaka-san likes sushi.
彼女は好きだ I like her.
彼女は好きだそうだ （I heard that) She likes (something - from context).
"田中さんはお寿司が好きだ" is incorrect? It never crossed my mind that it was, but it seems to make sense based off of your description above. My question is that does this hold up for questions as well (寿司が好きかい?) or is that only for simple declarative sentences? And if so, why the need for "なようだ" if it especially translates into "seems like~"?
It is because adjectives like 好き 嫌い 怖い are for 1st person feelings only. We cannot form a declarative sentence with these adjectives directly to describe feelings other than the 1st person (technically). You can directly use it in questions (e.g. 田中さんはお寿司が好きですか) but one can never 100% sure about the feelings other that that person, so adding 好きそうだ/好きなようだ adds uncertainty to these feelings.