The difference is one of authority. Goldman's authority to kill isn't accepted by society at large, whereas the due process of election, appointment, induction, training, and periodic evaluation is so accepted. You can argue about whether or not that acceptance is a good thing or a bad thing, and Goldman likely felt it was a bad thing, but that acceptance is the fundamental difference.
The presumption that individual violence is wrong follows from this systemization of it. When it wasn't, we did commit individual violence with no reason. This is rapidly apparent in watching children interact without intervention: they exhibit the full range of human extremes in both cooperating spectacularly but also in conflicting violently. By systematizing it, we've made it rare and remarkable.
And because it stands out, it's now considered wrong.