It follows from Christian theology (imago dei) but that's increasingly losing ground in the West. If we're just agglomerations of atoms why should I believe that all human agglomerations are equally precious?
Post-enlightenment philosophy holds that these are two different domains [1], and conflating them is a category error. You believe we're agglomerations of atoms because the experimental evidence makes this the most likely explanation.
You believe that human agglomerations are equally precious because you believe that human agglomerations are equally precious; no reason is needed, and indeed, no reason can logically be given.
Instrumental values can have arguments for and against them. Only terminal values are "protected". I'm not sure that considering all people precious is a 100% terminal value, it seems at least partly a game-theoretic convention.
Self interest. You can't control other people, but you can participate and propagate (hence strengthen) social norms. Unless you believe you and the ones you care about will always be in power, it's good insurance to propagate the belief "all human agglomerations are equally precious". (Same exercise as "which world do you want to live in as a rational being")
Imago Dei is basically "I am precious because I am precious to God (as is all life, especially humans)". I could also say that I am precious because I am precious to my parents.