Refused for UK visitor visa as a student, because I was considered "unemployed" [closed]

Recently I applied UK visit visa twice from Indonesia, and both applications were refused. I understand the reasons for refusal, but what bothers me is that in both refusals, UKVI mistakenly assumed that I am an unemployed.

I am a student. I clearly stated that in both application forms. I also provided a letter from my university confirming my student status and permission for short leave to visit UK.

How can I correct their mistakes? I tried to find information about appealing, but my problem does not fit with the reasons for appeal. Do I have to re-apply only to correct their mistakes? I am thinking about my record in their database, which might influence my credibility for future applications.

Additional information Thanks for all your responses. To be clearer, I applied for UK visa together with my brother, who is unemployed. In my case, UKVI assumed my brother as a student and me as unemployed. In the refusal letter, regarding me, UKVI said that because I am unemployed, so there is no any ties with an institution, they are not convinced that I will return at the end of my planned trip. In my brother's refusal letter, UKVI said that because he is a student of a university (in which I am actually in), he failed to provide a letter of university which says exactly from when until when the university give a permission of leave. So, this is, in my opinion, simply the carelessness of UKVI to confirm the information in the application form, so my brother's and my identities were swapped. In the second refusal, this issue of studentship and employment is repeated again, which unfortunately I forgot to explain in my second application. So, UKVI might not look carefully at the application form and other supporting documents, but consider more on the previous refusal letter. As I stated earlier, I don't mind with the refusal. My concern is how to correct the information about this swapped identity. Do I have to re-apply to correct this? Or is there any other way to do so?