The classical discussion of the prohibition of taking life and of injuring a limb examines the direction of dependence between their rulings. Both acts being prohibited does not by itself prove that the legal basis of one is the cause of the other.
The conditions and outcomes of retaliation for killing and for injury are not identical. If an analogy depends on making one a cause of the other, qalb can reverse that relation to expose an unsupported assumption.
These are historical legal categories discussed within a judicial framework; no permission for private enforcement follows from the analogy.