I'm sorry, but this is a terrible example sentence. Who on earth would refer to walking their dog as "taking a walk with" their dog? The dog has no independence. It doesn't join you for a walk the same way your friend Julie might.
The example sentence should be changed to: Anne et Antoine promènent leur chien.
You can have the same answer choices, but the correct answer would be "Anne and Antoine are walking their dog." Which is a sentence you might say in real life, as opposed to "They're taking a walk with their dog" which no one said ever.
Also disagree with the bold statement that no English speaker anywhere would use the expression you object to in the first place. It is a very big English speaking world, and I can assure that the phrase is certainly in use in at least some parts, especially nowadays when younger generations may indeed give their dogs ‘human names’ and refer to them in human terms.
Many a pet owner recognises that their pet is in charge !
Forgive me, but you are completely missing the point.
The lesson is explaining the verb se promener and here is an example from the lesson:-
"Je me promène dans le parc avec Julie.
The very sentence structure that is causing you some grief is exactly that expressed above to highlight the specific action (as it would be in English) of se promener as a verb.
I hope this helps,
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