honestly, i'm about to graduate college and i still have trouble with stuff like "why did the other done so and so this way" kinds of questions. keep trying your best. write a draft and ask your teacher to work with you on improving it. or have people go over your work with you when you finish and before you turn it in. brainstorm ideas with other classmates. after reading a book, discuss it with other people, preferably people in your class or those who've already read the book.
and keep writing! i think the problem isn't necessarily writing skills, but analysis, like you said. sometimes that's just not everyone's skill. i'm sure there are other things you are good at as well. however, you're right to try and improve your abilities.
i love to read and have an easy time writing, but i still hate the kinds of assignments you're talking about. so it's not completely necessary to be perfect at it to be a good writer or to be successful in life, or to get into college. so try not to stress and instead just do your best and know that that is enough. you will do better that way.
your writing here was not bad at all, and it wasn't for a professor or teacher or anyhing to read, so it wasn't necessarily even your best writing. so i think you're doing okay when it comes to being ABLE to write. it's being able to analyze and put that on paper.
i'd say just do multiple drafts when you can. if the answers other students give to questions make sense to you, then you CAN understand it. it's just that you're having a hard time coming up with it yourself. try to see how they came up with their answers. why did they decide that that was a good answer? what was it that made them think that way? then try doing what they do.
it's okay to not have the right answer in class. try joining in on the discussion, or asking good questions. maybe ask the teacher to clarify or say the question in a different way. maybe you are just not understanding what the teacher is looking for in the first place.
good luck!