So you agree with me.
Not quite acting like software
In what way does firmware not act like software? Software is merely a series of instructions.
but not something you could unscrew and remove, either.
Not true. As I pointed out many times the ROM-BASIC was part of the IBM PC firmware - it was later reverse-engineered as an executable so clearly firmware can be unscrewed and removed. Some firmware can not be executed like a regular programs because it addresses low level function (like disk io) or it controls a specific device. It is still software - a series of instructions.
By "unscrew and remove", I meant in the sense of a piece of hardware. I agree with you that firmware is a set of instructions, hence, software. The intent of firmware, however, is to be treated differently on a day-to-day basis from other types of software, which are routinely started up, shut down, and generally used as applications. Firmware, on the other hand, seems to me to operate on more of a fundamental level, directly instructing and controlling hardware or systems on how to be that particular hardware or system.