There is one important part of taxonomy that is not arbitrary, however. The classification should be hierarchical, reflecting the evolution of the tree of life.
That's absolutely arbitrary too. The tree of life is a lie.
...or at least a very simplified model that breaks down as you move towards simpler and simpler forms of life. That's because horizontal gene transfer is a thing, and when you go all the way back to prokaryotes, there's so much of it going on that any "tree of life" is a statistical picture that's valid only for a select genetic marker that's used to trace dependencies. Pick a different marker, you'll get an entirely different prokaryotic tree of life.
