Why wouldn't a professor allow a student to record audio of his lecture?

This is a subjective question, but common reasons I have heard (and reasons I would have) include:

  • Fear of students editing records to manipulate what you said
  • Fear of having a mistake you made taken out of context and spread widely
  • Concern that it encourages students to not pay as close of attention
  • Concern that students will not feel they need to attend class if they have acceess to the lecture outside of class.
  • Concern that students in the class will not feel as comfortable asking questions or contributing to discussion, since they are also being recorded
  • Institutional concern about a course's lectures being widely distributed online, when in fact these lectures are for (paying) enrolled students--a type of "intellectual property" concern

Edit: Also, you might want to be aware when bringing up problems getting easily distracted in the class, a professor could take that somewhat personally. Many committed teachers go out of their way to try to make their class as interesting and engaging as possible. If a student asked to record lectures because they are getting distracted or zoning out during class, one may not hear: "I am trying to do this to improve my learning;" but rather: "I am trying to compensate for your short-comings as a teacher". Not all instructors will feel this way, but that's just something to keep in mind as you broach that conversation.

Edit2: There's a lot of discussion in comments that my last comment about socially navigating the question: it is very true that many teachers may not care. However, trying to frame the request more explicitly as "this is a thing I am doing to improve my learning" could be beneficial in making your instructor agree.

One more to NMJD's list: privacy of other students. Enrollment and participation in a class is FERPA-protected in the United States.

Students may share comments or information that they do not want shared outside the classroom.

For example, a religious student may share doubts about their faith or LGBT status. A student may not want others to know that they are taking a class but their voices or faces may appear on the tape or video. An engineering student may ask a really stupid question or give a totally wrong response that they do not wish transmitted to the outside world and future employers. etc. etc.

I understand that you want us to play devil's advocate to help you think ahead and prepare for the conversation. Good thinking -- it's good to do your research ahead of time.

I would like to play devil's advocate at a more fundamental level, though.

I do not consider myself to be disabled in any form but I do find it difficult to concentrate in class. I lose focus too often and have difficulty recalling concepts taught during class.

Perhaps you have already had a good evaluation to find out why you lose focus often and have difficulty recalling concepts taught in class. But if you haven't yet, then I would encourage you to do so. Your question did raise a red flag for me, and made me wonder what might be behind your difficulties with focus.

If the evaluation were to find some clear reason, that could be documented to the satisfaction of your university's office for students with disabilities, you wouldn't have to struggle all on your own to get accommodations you need.

And now back to your immediate concern. I would guess that common underlying reasons for refusing would be self-consciousness and fear of the unknown, if the instructor had never had the experience of being taped while teaching.

If this is the case, it might be helpful to try it out in office hours, with permission. Another benefit of visiting office hours would be that the instructor would get to know you better, would see that you're working hard and doing your part, and would find you more trustworthy.