If your teacher said "I couldn't go" is incorrect, then your teacher was wrong to that extent. "Could" is the simple past tense of "can".

nobody ever actually says "it's raining cats and dogs" except in children's books. XD if you're being extreeeeeeeeeemely strict, "couldn't" implies that you don't have the skills or capacity to do something. If you broke your leg, you "couldn't" go. If something else was stopping you, you "weren't able" to go. but, I mean, I must've had ONE teacher tell me that maybe ten years ago. and I only remembered that because of your question. nobody in real life, in everyday written text, on government documents, or in native conversation would ever, EVER, make that correction. "i couldn't go because it was raining" is perfectly correct. whoever your teacher is, they're being way too strict for what is practical.

Actually, both are incorrect. The correct way to express this in English is: It was raining cats and dogs, so I DIDN'T go to the stadium. We don't use "can" as often as you do in Japanese.

Both answers are right. In fact, because you used an idiomatic phrase, then "I couldn't" is actually more suitable (to me). Using the "to be able to" grammar is just messing about. You need something colloquial and direct.

I think it's just the fact that "I couldn't go" is used more in conversation, but "I wasn't able to go" would be more appropriate in writing.