Re: AKA Libertarians
"Well , you could just call yourself a Computer Programmer, and leave the engineering to the Engineers."
You've assumed that the code the OP was talking about was intended to run on a computer.
As an engineer myself, now into my 3rd decade of working on bare-metal embedded systems development, I don't see the slightest problem for people in this sort of role describing themselves as "software engineer", "firmware engineer", "embedded systems engineer" etc. Nor was it a problem for my university, who alongside the more traditional "Electrical & Electronic Engineering" degree I was on, also offered one titled "Microelectronics and Software Engineering". Which, in hindsight, is the one I probably should have taken given how little classical electrical engineering I've done since then, but that's another story for another day.
Because when you're working in that sort of role, you're not bashing out code to run in a nice clean abstracted OS environment where you almost certainly don't need to care much/at all about the underlying hardware, you're writing code that needs to be tailored to the specific capabilities of the target platform and making use of your experience with the particular microcontroller to provide feedback to the hardware designer (if that's someone else and not just you wearing a different hat on a different day) as to how the hardware could be tweaked to make the code more efficient.
And in such a role, describing yourself as a "programmer", "software developer" etc. is more likely to have you eyed with suspicion as to how much embedded coding experience you actually possess...
P.S. I'm neither outraged, nor have I cast any downvotes here, but I hope that doesn't disqualify me from responding to your request for an explanation :-)