I have noticed a similar problem with my female cat. She generally has a soft and fluffy coat, but the fur along her spine has become coarse and is significantly thinner than the rest of her body. As you described, I can brush her hair to the side and see her bare skin.
I actually just brought her to the veterinarian today (for an unrelated issue) and asked about this. We came to the conclusion that, in my cat's case, it is most likely either a seasonal allergy-related issue or an issue with the transition from her winter coat to her spring coat. She is an indoor cat, but still goes through quite a seasonal transition. She had the same issue last spring, but I assumed it was from "over-grooming" at the time.
If this is the first spring that you have had your cat and you live in an area that undergoes seasonal changes, then it could be the same problem. In which case, you just have to wait it out for a couple of weeks and you should see some improvement!