There's an argument that the structurally correct but semantically bizarre sentences are very helpful language-learning tools, and I'm inclined to agree with it. I have no objection to this sort of sentence - it's memorable and it teaches grammar divorced from meaning. I'm not trying to learn a phrase book after all.
I agree that this should not be regarded as a phrase book, but a bit more realistic, please.
I don't mind sentences with counterintuitive content. But I do wonder whether the ownership dispute of the tea is between my cat and you, or my cat and your cat. I'm inclined to think both are possible. In angrezi, it depends on where you put the accent... this is MY cat's tea, not yours vs. this is MY CAT's tea, not yours. I wonder if the same is true in Hindi.
This sentence makes very little sense in English, so might mislead some learners who thought (like I did) that they heard the Hindi wrong. How about "This is my cat's food, not yours"?
I agree with you, I have seen this kind of ridiculous sentences in different languages from Duolingo. I cannot object the grammar but as a foreigner seriously trying to learn the language I question the utility of this. Even if I know the words or the structure my brain is saying "It is not possible".