Bloomberg Software Developer interview questions

I applied online and they got me straight to a video interview (not sure if because I had previously applied for an internship or it's the standard procedure). I passed the first interview. I then got an email that I made it to the virtual interview day which entails 3 interviews (algo, system design, HR) but they are eliminatory (meaning that if you do not pass one of them, you do not take the next one). I had my first algo interview that was a fairly easy problem which I solved in 15 minutes and then he asked a follow-up which I also managed to solve before the end of the interview and he gave me the approval for the solution. The downside was that whenever I was writing the code and said I would go back to the condition at the end to correct it if needed, he never actually let me do it and was saying that it may be incorrect, which I pointed out that I knew (as I had already said and explained before) and I was planning to fix it once my function was fully written (which I did). I was expecting that after this I would go to the next one (which would have been system design) since I had solved and coded two problems in the time I had, but I got the email that I was rejected. I was taken aback by this so I asked to schedule a call to receive the feedback for the interview (it is allowed) but the recruiter has yet to get back to me. I have been told that you can contest and maybe retake it if you feel like it was unfair to you, but I do not plan to.