Many rounds get their start in the military - .30-06, 45-70, and do substantially more damage to a human body than the 5.56 round, not because they started in the military, but because of ballistics. Other rounds start off in the private sector and get brought into the military, like the .308 and 6.5 Creedmoor.
There is nothing particularly deadly about the .223 round that isn't common to all rifle rounds, particularly larger calibers. Rifle rounds are deadly to living creatures, human or not.
The military has, time and again, dropped and adopted rounds balancing many interests, not only effectiveness on the battlefield, but also the logistics of moving ammunition from point a to point b. Sometimes the latter comes at the cost to the former. Recall that when the 5.56/223 round was introduced, it was panned as being completely inadequate for human targets. It was replacing a .30 round that had more stability in flight, more range, and more punch when it got there. Those rounds replaced a .45 caliber round before that.
The reason people say, "not an assault rifle," is because in the gun world that has a particular technical definition that the AR-15 does not meet. Using the term outside of its technical definition is nakedly an appeal to emotion for political purposes. There are more sober ways to make the gun ban argument without resorting to this language, but I'm not holding my breath. Fearmongering is effective.