Why is the liver able to regenerate?
The liver regenerates because it complies to the liver homeostasis rules.
The hepatic functions are necessary to maintain body homeostasis.
Hippocrates may have understood homeostasis when he mentioned the rules of "nature" ("physis").
In the Hippocratic Corpus -- the ancient collection of medical texts attributed to the father of medicine -- we can find the following aphorisms:
"Nature is the best physician", and "Natural forces [physis] are the healers of disease". [Corpus Hippocraticum].
And one modern study explains:
"The complex challenges of the liver toward body homeostasis are thus always preserved by complex but unfailing responses involving orchestrated signaling and affecting growth and differentiation of all hepatic cell types".
[source: Michalopoulos, G.K. Principles of liver regeneration and growth homeostasis. Compr Physiol. 2013 Jan;3(1):485-513. doi: 10.1002/cphy.c120014 ].
[Also see: Hepatostat: Liver regeneration and normal liver tissue maintenance, Hepatology 65(4) · December 2016. DOI: 10.1002/hep.28988 ].