You're assuming the language is inherently symmetrical by focusing on the technical meaning rather than the meaning derived from usage. "Black Lives Matter" is

You're assuming the language is inherently symmetrical by focusing on the technical meaning rather than the meaning derived from usage. "Black Lives Matter" is a slogan. It means "Black lives also matter." If someone wanted to respond to that by saying "White Lives Matter", they would be egregiously missing the point, no? Creating conflict from something that they presumably don't disagree with? And why would anybody do that?