I recently realised that a lot of popular misconceptions about language evolution derive from uncritical use of the "family" metaphor. In families, a person has kids and then stays around, alongside the kids, for many years... they may live to see their great-grandchildren. The parent and the child may show a family resemblance, but will certainly be separate individuals. If you're told that languages come in "families", and "descend" from past languages, then it seems perfectly reasonable to imagine those ancestor languages lingering on alongside their descendants, and to imagine that the minor changes occurring daily within the language you speak are completely different from the sharp discontinuities that would have to occur for a new language to emerge.
But languages don't work that way at all: a language's "descendants" are (with rare exceptions) simply the various results of its own changes in the mouths of various communities. It's usually meaningless to talk about one living language being the "ancestor" of another one; in such cases, both are descendants of the same ancestor, even if (as infrequently happens) one has changed significantly less than the other. (Revived languages, like Sanskrit, are arguably an exception.) The same mistake is frequently made in popular understandings of biology, for the same reason; people imagine that chimpanzees (say) are humans' ancestors, when in reality the very fact that chimpanzees exist alongside humans proves that, while both species share a common ancestor, that ancestor was neither of them (or, looking at it another way, has equal right to be described as either of them.)