The existence of quines is a nice proof that biology isn't magic. Consider an alternate history in which computer science develops before organic chemistry. Prior to the development of organic chemistry, some common beliefs about life were, for example, that living matter was fundamentally distinct from nonliving matter, and life could not arise from non-living components; and that obviously no mechanism could contain its own description, so the only way biological reproduction could work is if, say, sperm actually contained miniature complete organisms, which in turn contained even smaller complete organisms, in an infinite regress (see https://en.wikipedia.org/wiki/Preformationism).

If, however, you can construct a quine, those beliefs are no longer "obvious". If you can write a program that replicates itself, then you can build a machine that replicates itself--and living organisms might well be such machines.