"I do not like airplanes."
Yes, it should really be が here because the full sentence would be 私はひこうきがきらいです 。私 (I) is the topic and is followed by は while ひこうき (airplane) is the subject of the sentence and is followed by が. I was taught (and Genki 1 says) to usually just use は when contrasting 2 or more items, such as 肉は好きですが、魚はきらいです (I like meat but I don't like fish).
You can use ga for both things you like and dislike but you often use ha to emphasise what you don't like. So "watashi ha hikouki ga kirai desu" means "It's me who dislikes airplanes." (as opposed to my friend) whereas "hikouki ha kirai desu" means "It's airplanes I dislike." (as opposed to boats).
In English the thing you like/dislike is the object of the sentence but in Japanese it's the subject, that's why you can use "ga" not because it's the thing you like/dislike. In Japanese, the sentence means "Airplanes are dislikeable." with "by me" implied.
This may be 2 years later, but it's for those that will come here.
は is used for emphasis. To emphasis the "negativeness", and also as a contrast marker, as in "I hate this, as opposed to something else".
(私は)飛行機は嫌いです - There's nothing wrong with this sentence. The first は is a topic marker, the second a contrast marker;
(As for me), it's airplanes I dislike. (as opposed to something else)
飛行機 is easy if you divide it:
飛 = to fly (飛ぶ)
行 = to go (行く)
機 = machine, mechanism
I just got this after two examples of food where we used が きらい. Makes me wonder if the food examples were just personal preferences, so わたし は would be implied, while the speaker here feels that as for airplanes, they are just plain bad and should be hated by everyone? Or is this a food vs non-food thing?
I think that should also work
The question here uses "dislike" rather than the negative "do not like" for some reason. Probably just to teach a new vocab word, though the English should probably reflect a bit more that they're looking for a different word than the negated version of one we learned a while ago.