We lost a lot of historical records between late antiquity and the early middle ages. Most devastating for Italy was probably the Gothic War.
Then the records that were in Constantinople were also lost, not only by the fall of Constantinople itself but also by the sacking of it by Christian crusaders.
Lots of records that could have shown such a descent are lost.
Now Confucius was an important historical figure.
It's not surprising that he is one of the few cases where an uninterrupted descent could be true. If Jesus or Caesar had a family line run into modern times or if the Papacy was hereditary, we might have such a line for Western civilization as well.
Then the records that were in Constantinople were also lost, not only by the fall of Constantinople itself but also by the sacking of it by Christian crusaders.
Lots of records that could have shown such a descent are lost.
Now Confucius was an important historical figure.
It's not surprising that he is one of the few cases where an uninterrupted descent could be true. If Jesus or Caesar had a family line run into modern times or if the Papacy was hereditary, we might have such a line for Western civilization as well.