Because ideas are not automatically invalidated depending on the mouth from which they’re communicated. To assert so essentially turns into an ad hominem rejection of it, which speaks not to the validity of the assertion, but merely casts blame on the subject itself. Likewise, non-violence as a ‘white privilege’ is not particularly substantiated in any way, and is actually fairly easily refuted with a cursory glance outside of the Western-Anglo sociopolitical sphere. But this is plain empiricism, which is easily overlooked.
If they were a little more specific or careful with their usage of terms, and contextualization, though, you may be able to construe it more meaningfully: “Do violence never, says privileged white dude [in the west, in the media, whilst empowering his system of domination]”. To make no demarcation among those you’re pointing criticism at is irresponsible at best, and grossly counter-productive and dangerous at worst. This could constructively be critiqued from a standpoint which acknowledges that Western media continually reinforces expected forms of behaviour whilst simultaneously negating them in action; this is entirely valid. But the target, to be sure, is the State/Media discursive complex which embodies the agendas of those in power, who are predominantly white and male.
In that quote, the notion that whites are inherently, ironically hypocritical for endorsing non-violence is clear enough; however, that non-violence is impossible if you are non-white is not the necessary conclusion, but is definitely the tacit inference. What it seeks to do is link the availability of non-violence to white-privilege—and leave it there, isolated—an assertion that can be attacked from a multitude of angles. But the most poignant, or relevant of those, I think, is the admission we must make that above all, violence is a choice. It is entirely active and does not necessitate mutual engagement. And herein, too, lies a hypocrisy: obviously, the angst against white privilege is from the violence that whites have historically done to non-white persons, histories, and cultures. So here is a two-way freedom, where violence is readily available to all, and a supposed one-way freedom, where non-violence is ostensibly available only to some, by virtue of a phantasmic necessity that non-whites are unable to give up in order to exercise non-violence. The implication is that non-whites are either unable to commit to non-violence, or are forced to commit violence.
The deeper problem, however, with this kind of rhetoric is in linking privilege—a passive, non-participatory form of social status (you aregiven privilege; it is not acquired [by you]; something has been bestowed upon you for which your own efforts are not responsible; it’s not highly dependent upon agency or activities of choice)—immediately with the permission-by-necessity of violence, an active, responsible agent that is entirely by choice, excepting, of course, in cases of defense. The privileged per se are not justified targets of violence merely as such.
To explicitly state the message that is inferred from the logic employed here would be shocking if taken to its apotheosis. It would be somewhere along the lines of, “we, the non-whites, (either) cannot achieve non-violence [because we lack the means to do so], (or) [we] deny the validity of using it [because to do so would be to vindicate the status of the group that espouses it: white privileged dudes], and so defer to violence as the means to our emancipation (and cannot be held accountable for it)”. The conclusion is thus a frightening one, and not merely because I am a privileged white dude, but because it is indiscriminate and does not locate the direction of any of this violence, which may hint at some possibility of specific grievance and thereby recompense or Justice. [Speaking generally,] the vagueness of language and the occasional refusal to commit to its strengths, either to mask the fallibility of its message, or to manipulate the sentiments that may be drawn from its vagueness, leave open an infinite swath of interpretation. In this case, a not-too-hysterical interpretation may lead one to see it as an approval of violence as a principle in itself, since there is no included self-limiting principle in the message. (My axiom here obviously being that violence is not desirable—but I say that without reservation or qualification, for I do hold that it is an absolute principle which nobody, especially to the exclusion of others, should dismiss. To wit, I don’t hold that non-violence is good because it benefits me as a Privileged White Dude, but because it benefits everyone—an axiom that this quote will not admit. It is the emotional appeal of this quote which makes it so dangerous since it gives way to violence as a transcendental principle.)