If life indeed has a common origin via evolution, as Darwin suggested, then there are two ways to classify life consistently: objective, ie using an orthogonal system like Linnean systematics, and subjective, ie, using a “flat” system like cladistics.
The objective classification is consistent with regard to the objects of the classification, eg, “organisms”, whereas the subjective classification is consistent with regard to the subjects (ie, classes) of the classification, eg, species.
The problem with the objective classification is that there are several just as consistent such classifications of such an origin of life, whereas the problem with the subjective classification is that a flat classification is ultimately paradoxically contradictory, as Russell’s paradox demonstrates.
It means that none of these kinds of classifications can arrive to a single “true” classification, and that they only differ in that the objective classification is ambiguous with regard to the origin, whereas the subjective classification is paradoxically contradictory.
This problem makes belief in a common origin of life difficult by meaning that there is no way to describe such an origin both consistently and unambiguously at the same time. It is then important to understand that this problem is purely artificial, ie, an inherent impossibility in conceptualization to combine objects and classes both consistently and unambiguously at the same time. It has nothing to do with whether life has a common origin (via evolution) or not. The problem is thus no obstacle to a belief in that life has a common origin (via evolution), ie, doesn’t mean that the belief inconsistent.