"Chicken with rice" and "rice with chicken" are usually not the same thing. "Chicken with rice" supposes that your main dish is chicken and you're having a side dish of rice with it. "Rice with chicken" supposes that you're having a rice dish with some chicken added to it.
I agree. There are lots of times when Duo counts us wrong for not adjusting the presence or absence of the article to account for the difference in languages. Other times - suprise! - you better have it match exactly. I'm reporting this one, as you just wouldn't say it this way in English.
I was also wondering about gerund use in this lesson. I found an explanation but I'll be darned if I understand it.