In order to further understand this, I found the frequently-cited and fairly influential article entitled #BlackLivesMatter: Epistemic Positioning,
Challenges, and Possibilities by Catherine L. Langford and Montené Speight helpful. They have looked at particular movements sparked in response to the Black Lives Matter slogan, including 'White Lives Matter', predominantly on social media in the form of hashtags but also where these have spilled over into demonstrations or counter-protests.
Generally, on the subject of counter movements, and in particular on the '#WhiteLivesMatter' movement, they have this to say:
Movements counter to the #BlackLivesMatter movement play upon the
phrase, including
#AllLivesMatter, #BlueLivesMatter, and #WhiteLivesMatter. These movements engage in a politics of erasure, shifting public focus from
violence and discrimination against Black lives in an effort to
re-center Whiteness. Each of these hashtags co-opts the
#BlackLivesMatter movement by negating the Black race in favor of all persons, police officers, and White people. The first ignores the
importance of race, the second rejects race in favor of
institutionalized force, and the third decries reverse discrimination.
[...]
#WhiteLivesMatter attempts to re-center White privilege in a straightforward fashion by extolling the White race and denigrating the Black race. Although Nakayama and Krizek tell us
that “white” remains “invisible as it continues to influence the identity of those both within and
without its domain,” as it occupies “a largely unarticulated position,” the #WhiteLivesMatter
does not allow the values of whiteness to remain invisible or unarticulated. Commentary on social media, at counter protests, and on flyers distributed in residential areas, proclaims White
Americans need to pay attention to events, stand up for themselves, value their own lives, and
realize that the news media will not cover discriminatory acts against White individuals.
[...]
These counter movements are just three examples of rhetorical plays on the
#BlackLivesMatter movement. Others include:
#HispanicLivesMatter, #LatinoLivesMatter, #BrownLivesMatter, #AsianLivesMatter,
#FetusLivesMatter, #BabyLivesMatter, #UnbornLivesMatter, #EveryoneMatters,
#PoliceLivesMatter, #SouthernLivesMatter, #AmericanLivesMatter, #ChristianLivesMatter,
#LGBTLivesMatter, #MuslimLivesMatter
These are only a few. Not all riff on the hashtag in an effort to erase race, reify institutional violence, or declare reverse discrimination. Many plays upon the hashtag advance racial rights, pro-life beliefs, and people of different identities.
The ones discussed above, however, seek to invalidate the #BlackLivesMatter movement by re-centring whiteness. Whether by triumphing the
value of all life, asserting the importance of the police, or decrying reverse discrimination, the
rhetorical consequences of each is the same: to ignore, and thus to invalidate, the grievances of
African Americans. The use and proliferation of alternate hashtags attempts to shift the focus
from #BlackLivesMatter to maintain whiteness as a centralizing epistemology because no one
critique can be sustained long enough to challenge it.
They argue, then, that the use of the term 'White Lives Matter' seeks to co-opt, and, perhaps, to minimalize the Black Lives Matter movement by re-centering 'Whiteness'. They argue that this attempts to frame the systemic oppression that Black people have faced in the past, and still face today, as equivalent to that faced by White people - something which is disingenuous at best.
In addition, they examine the actual movements and demonstrations that have spawned from the use of this phrase and find dog-whistle propaganda attacking Black citizens, the media, and calling on White people to 'be proud of their "people" and heritage' - something which out of context sounds fairly innocent. The argument that the phrase is racist because someone who is racist uses it is possibly an example of an association fallacy, but especially in a highly charged situation like this, it is necessary to take this factor into account.
The use of #WhiteLivesMatter on Twitter rearticulates the negative
stereotypes of African Americans presented in media. Black citizens
are characterized as “thugs,” “racists,” unintelligent, and
“terrorists.” White citizens are “under attack,” “oppressed,” and
should be proud of their “people” and their heritage. The media are
“hypocrites” for covering up crimes against White individuals by Black
perpetrators. Most of these appeals rely upon the false dilemma
fallacy, contending that one group is good and the other is bad, or
that to advance the rights for one group means that you do not value
the rights of another. Following an incident in which
#WhiteLivesMatter flyers were distributed to personal residences in Connecticut, for example, one blogger posted, “Black lives matter, and
White lives don’t. The sentiment has been noted,” and, “Black lives
matter. No one else’s lives matter. If you dare to ask why this is or
disagree in any way, you are evil.”