Why measure entanglement as a branchial distance?

Because entanglement in real physics is a matter of degree — states can be a little entangled or strongly entangled — so the model reaches for a branchial metric (a distance) rather than a yes/no link. The proposal is that a recent common ancestor means small branchial distance and strong correlation, while a distant common ancestor means large distance and weak correlation. [conjecture] This branchial metric is conjectural, posited by analogy with ordinary physical distance, and is not a worked-out result.