A clarification: the argument I'm saying we could make is a factual-level argument of "the
reason humans
believe that 'human life is precious' is because those humans who don't have long since killed themselves. Its structure is similar to Descarte's 'cogito ergo sum', something like:
"In order for someone to have a belief, they must exist. In order for them to continue to exist, they must not have taken any action in the past that would lead to their death. People who believe that human life is not precious are significantly more likely to take actions that will lead to their death. Therefore, people who believe that human life is not precious remove themselves from existence at a higher rate than those who believe human life is precious, and so the vast majority of people will believe human life is precious."
You can quibble with the premises and I won't defend them, but you would agree that this argument takes the form of a syllogism and hence is a logical (if possibly false) argument. My overall point is not about whether human life is or isn't precious, it's about the distinction between object-level and meta-level. On the meta level you can make a logical argument, from falsifiable premises, about why people might believe the statement "Human life is precious". But on the object level, that statement is a value judgment, and so that statement can't be approached with logic in any coherent way. You can argue about the truth or falsity of whether & why people hold certain values, but you can't argue with the values themselves. (Logically, at least; you can always argue using various fallacies like argumentum ad auctoritatem or argumentum ad baculum. Indeed, applying the results of your analysis of why people hold beliefs to whether the beliefs are right is an example of the ad hominem fallacy.)