If a system administrator misconfigures a router and damages our information infrastructure, is that any less relevant than someone sticking C4 to the side of a power transmission tower to cause a similar amount of damage?
One word:
Intent.
Intent matters. That's why we punish people who kill someone or cause property damage, etc., intentionally, and don't punish those who do the same things, but don't do so intentionally (and also don't do so because of negligence or reckless disregard). It's the same result: someone is dead, property is destroyed, etc., no?
(Ahh, the gray area -- negligence. What if that network admin can be proven "negligent"? Well, I'm not a lawyer, but the general answer is still intent.)
So, intent matters. We care when someone is actively and purposefully trying to do us harm. That's also the simple answer to the question of why we prosecuted a "war on terror", and why we don't have a war on ladders, a war on lightning, a war on car accidents, or any manner of other things that can kill people. Those things are accidents. Sure, sometimes there is negligence peppered in, and there is immeasurable complexity beyond how I've distilled it down here.
But what of cyber -- when we talk of something like "neglecting" to secure a router (secure how? by whose standards? by what measure?), and it is compromised and real, quantifiable damage is caused, who is at fault: the admin, or the attacker? There are two general camps here: those who believe that the admin and/or router vendor is at fault, and those who believe the attacker is at fault. The truth usually lies somewhere in between, but on the friendly side it's less about "fault" and more about responsibility.
If you leave your house unlocked, and someone comes in and burns it down, is that your "fault"? There are all sorts of ways to argue this, but the bottom line is that while you might have a responsibility to protect your property in a sensible manner given your circumstances, it's still the attacker who is solidly at fault, and subject to punishment.
When it comes to cyber war it's a complex landscape. Civilian, academic, financial, critical infrastructure, government, and military systems are all interconnected. What's the difference between cyber war, cyber espionage, cyber crime, cyber terrorism, hacktivism, or simple malicious hacking? We as a society rely on these systems. We want to be protected, but we don't trust the government to do it. Perhaps that will always be a shortcoming of free and open society in this and other realms; the benefits of open society certainly outweigh the risks. But that also puts us at a distinct disadvantage to those who wish to attack us, whatever their motivation and affiliation.
As for how we trust the military? By learning what the capabilities, techniques, and threat landscape looks like. Sure, some information is classified or so arcane as to be boring, but it's all out there. How can we trust the military to properly execute any military action -- to maintain air superiority, to drop a bomb, or to capture a city? Because, politics and personal feelings on any particular issue aside, these things are well-understood concepts. Cyber might not yet be as well-understood, but even for all the obfuscation, confusion, and hype, it's a realm that also has rules and can be understood.
Militaries have been deceiving their adversaries for literally millennia. Cyber is new, but it is no different. Yes, it is powerful, and a single person or small group can create havoc far disproportionate to their manpower. But we've had many significant force multipliers over the course of warfare. We develop new tactics, new intelligence methods, new techniques, new capabilities.
If an adversary attacked a US civilian asset militarily, is it not the job of our military apparatus to protect us...? It seems we have gotten to a point where people believe it is laughable to "trust" the US government or the military, when there is egregious oppression, suffering, and death at the hands of repressive governments elsewhere in the world. Some people say the government has forgotten the Constitution. I'd say that, with the aid of the echo chamber that is the internet, many people have utterly lost their perspective. The irony, I suppose, is that adversaries will take advantage of that, too...