National Math and Science Initiative Manager, Data & Analytics interview questions

Pre-recorded video interview where I answered ten questions. They gave 30 seconds to read each question and then 3 minutes to record an answer. Then I was given an hiring exercise to complete. They were very communicative and got back to me within a week at each step. Unfortunately, I didn't get an offer (I really wanted this job!) and when I asked for feedback they said it is their policy not to provide any feedback. This was very disappointing and really soured the whole experience. Fine, I didn't get the job, but I want to be better and have no idea why I was rejected. They get a thumbs up for their good communication and reasonable questions, but a thumbs down for no feedback.