I just failed this one in a test. Why it is not "We take the dog for a walk every morning"? Why continuous tense should be used?
You are correct; your teacher is wrong. When describing actions that occur on a regular basis, it is more common to use the simple present:
I play tennis every day at noon.
Every Tuesday I wash the dog.
She brushes her teeth first thing in the morning and last thing at night.
And so on. You might use the present continuous if the action occurs simultaneously with another action:
Each morning, at the moment the sun rises, we are usually walking the dog.
But this is a very specific and unusual case, where I really want to emphasize what is happening at a particular moment. In most cases, it would be more natural to say:
We take the dog for a walk every morning around sunrise.