Generally parents don't teach their children about grammar when they bring them up bilingually. One parent just talks in one language to the child and the other

Generally parents don't teach their children about grammar when they bring them up bilingually. One parent just talks in one language to the child and the other parent in the other language. At least that was the case for me. But I can very well image, that you gain a better understanding of grammar, when you speak two languages, almost by definition. This trick is also used in Natural Language Processing to improve part-of-speech tagging.