Why is it "This is not my coat" instead of "That is not my coat"?
"That is not my coat" would be "то не моє пальто."
In the tap the word tiles exercise, it didn't accept jacket, and required coat. In my dialect at least, the two words are completely interchangeable!
Just report it using the Report Problem button and it will be added.
But, in the context of this course at least, a jacket is a куртка. When Duo asks for an overcoat, I think it is specifically looking for пальто. That has been my experience in this course, anyway.