Why do cladists claim an impossibility?

I understand that the two facts that:

1. classification is ultimately contradictory (ie, Russell's paradox), and

2. cladistics believes in classification

means that cladistics is ultimately contradictory.

I'm just surprised that this fact has such a hard time to be acknowledged.

Why are there so few biological systematists out there willing to admit this fact? Why is this ancient belief in classification so hard to get rid of?

Is it because one third of all people assumes that classes are real, ie, are realists? If so, exactly what do they expect to gain by this resistance to acknowledge facts? Personal benefits?

Independently of cladists claim, fact is that classification (including "cladification") is paradoxically contradictory. It doesn't matter that all cladists agree about the approach, it is still inconsistent. Hundreds of billions of flies can't make eating shit tastefully, but can only lure people into eating shit.