Let me start with a bold blanket statement: Writing can’t be bad. The act of writing, just like the act of speaking, is solely meant to serve as communication. Technically, you don’t even need an audience either since you can communicate with yourself. This is to say, as long as you have a point and are attempting to get that point across somehow, you are accomplishing the art of writing! I, and many of my favorite writing professors, like to think of writing as a tool. Thus using terms like effective versus ineffective or functioning versus not functioning rather than good versus bad (because that objective outlook is useless) is more constructive.
All writing is attempting to communicate something; the only difference is how a writer goes about packaging their message. Yet, everyone has different preferences for what writing they are willing to read because it is a subjective art. No one can point at fanfiction and say “bad” let alone point at classics and say “bad.” These different styles merely serve the same purpose but to different audiences in different packages. I believe the same can be applied to your and anyone else’s writing!
Calling yourself a bad writer is most likely the root of your “bad writing.” Similar to any creative endeavor, it takes intentional practice. If you are not willing to put in the time to learn about writing skills then, of course, yours will be ineffective— but again, this does not mean you are a bad writer, just a less knowledgeable one. No one is born a great writer. To think this would discredit all the people who study writing for a living.
Whether creative, academic, or in between, writing can be learned. Teachers are more often harder than they should be on teenagers learning to write, but it can still be done. Do I think academic writing is the best, most useful writing ever? Absolutely not, but it does serve a purpose and has certain rules that guide it. Learn those rules and you’ll be golden.
The same thing applies to fiction and poetry, even more so, you simply can’t be bad at it. You write how you think and how you feel, and that will communicate your perception of the world to the reader. Now, maybe you think you are truly a bad writer simply because your writing lacks description or vocabulary or strong images, etc., but the key fact here is that: your writing lacks and not you. You can always learn how and what to add or detract from your writing, shape it like a piece of clay— however the hell you want. And the more experience you get, the more you’ll like your sculpture of words by the end!
My main point is to not identify yourself (and your worth) with your skillset. If you constantly bog yourself down by saying you are a bad writer, then it is inevitable that you will produce ineffective work because you aren’t allowing yourself the freedom to explore learning. One piece of advice that has always stuck with me is: the worst thing you write will always be better than the best thing you never wrote.