"We swim for half an hour every day."
At this point I think duolingo switches between "time">"subject" and "subject">"time" being considered wrong out of pure malice for its users.
Duolingo is correct. 游泳 is a separable verb. This is a complicated subject. It's best to refer to Chinese Grammar Wiki at https://resources.allsetlearning.com/chinese/grammar/Separable_verb or other sources.
I had always assumed that the grammatical rule was "[动][时间]的[名]", that is to say that you could only split verbs composed of a first character which is itself a verb, and the rest which is a noun.
- 我拉了一个晚上的肚子 (this one was an excuse I heard a native give to our teacher for being late in class :-p)
Here, 泳 is itself a verb, but not a noun, so this sounds unnatural to me. However as I've never been actually taught this grammatical rule I'm concerned that I might actually be wrong?
In modern standard mandarin, 泳 is always regarded as a noun.
It is not so in classical Chinese.
I disagree with the sentence. I dont think anyone would describe 泳as an noun in chinese. I would think that it should be 我们每天会游泳半个小时。
It is a separable verb
That is the verb 遊 yoú, meaning "to swim". It is the first part of the separable verb 遊泳 also meaning "to swim". The second part 泳 comes after the duration 半个小时的 describing the first part.