I don’t know where the idea that the “constitution” is “living” came from. The original quotes that use that word only use the word “living” to mean “still important” or “not to be ignored, no matter what sort of terrorism, Arabs and disgruntled members of the armed forces can wreck on America. (And nobody would disagree with that, now would they?)
Instead, people seem to attribute the words “living” to those who think that the “meaning” of the constitution changes over time. Unfortunately, they rarely give specific examples of who uses this phrase to mean this, nor do they provide detailed analysis of their jurisprudence.