Most guerillas don't fall under that definition any way. And there can be civil war regardless, Northern Ireland, various parts of Africa, Afghanistan, Syria...
(These are probably the reasons the cartels have for not becoming recognised belligerents: they likely see themselves as having unbundled the profitable aspects of violence from the unprofitable parts of governance.)
to switch references from the Geneva Conventions, consider the formal definition provided by Dr. Linebarger: http://www.gutenberg.org/files/48612/48612-h/48612-h.htm
> Formally, war may be defined as the "reciprocal application of violence by public, armed bodies."
> If it is not reciprocal, it is not war, the killing of persons who do not defend themselves is not war, but slaughter, massacre, or punishment.
> If the bodies involved are not public, their violence is not war. Even our enemies in World War II were relatively careful about this distinction, because they did not know how soon or easily a violation of the rules might be scored against them. To be public, the combatants need not be legal—that is, constitutionally set up; it suffices, according to international usage, for the fighters to have a reasonable minimum of numbers, some kind of identification, and a purpose which is political. If you shoot your neighbor, you will be committing mere murder; but if you gather twenty or thirty friends, together, tie a red handkerchief around the left arm of each man, announce that you are out to overthrow the government of the United States, and then shoot your neighbor as a counterrevolutionary impediment to the new order of things, you can have the satisfaction of having waged war. (In practical terms, this means that you will be put to death for treason and rebellion, not merely for murder.)
> Finally, war must be violent. According to the law of modern states, all the way from Iceland to the Yemen, economic, political, or moral pressure is not war; war is the legalization, in behalf of the state, of things which no individual may lawfully do in time of peace. As a matter of fact, even in time of war you cannot kill the enemy unless you do so on behalf of the state; if you had shot a Japanese creditor of yours privately, or even shot a Japanese soldier when you yourself were out of uniform, you might properly and lawfully have been put to death for murder—either by our courts or by the enemies'. (This is among the charges which recur in the war trials. The Germans and Japanese killed persons whom even war did not entitle them to kill.)
I don't know much about history but my understanding is this true only exists as long as it is convenient. The union didn't care for this role during the US civil war iirc
> So we train our military according to our values which renders them incapable of being able to maintain an occupation the way Chinese army or Russian army would be able to do.
The US military has been involved in all sorts of atrocities since the end of WWII, they just sometimes failed at achieving their military goals, e.g. Vietnam, and sometimes the government resorted to the use of other aggression tools, e.g. Cuba economic blockade.
if my maths are correct, we have 4,5/100'000 firearm homicides reported for the US.
This is less than the hot conflicts (including, per TFA, the mexican drug war), and same order of magnitude, but still less than iraq (7/100'000 in 2019).
However, it's an order of magnitude more than ukraine (0,3/100'000 in 2019).