How much time passed between your missing the exam and your emailing the professor about a makeup? If you didn’t do anything about it until it was clear you were going to fail the class without that test, and weeks had gone by, then I understand the professor denying the makeup. Personally I don’t administer makeup exams past 10 days, and I say so on my syllabus (it’s a common limit). The semester moves too quickly. Makeups also require the professor to spend time writing up another exam (to avoid cheating) and committing time to proctoring. It’s not that simple to do.
PS I missed your earlier response about the “no makeup” policy.