When it's bad, you want a VERY quick way of saying "shoot it again."
The "repeat" vs "say again" distinction is so ingrained that I've been out of the military for a decade and I still always, only say "say again." I don't do it on purpose, it's just part of me now.
I also use "say again" in regular conversation, and I've never been in the military. I picked it up from living in Singapore for a few years. Some of the short, simplified, not-always-grammatical phrases used in Singlish work great for communication - distinct enough to be understood despite the speaker's accent, few fluff words so that they can be parsed easily and spoken easily. Very close to the goals of the military and NATO in that regard.
We often forbid operators the use of "repeat", and we find ourselves using only "say again" on the phone, especially when the link is bad or the other speaker difficult to understand. Imagine speaking to a Pakistani or a Portuguese over a satellite phone.
That actually explains why quite a few people I know tend to use that form in a way that, to me, sounds pretty rude - it's probably just natural for them.
Fantastic. I was just telling the commentor before you that I do not have a military background. I'm glad you could weigh in. That makes complete sense.
The "repeat" vs "say again" distinction is so ingrained that I've been out of the military for a decade and I still always, only say "say again." I don't do it on purpose, it's just part of me now.