Why does cnidarian have a silent “c”?

For the same reason knight and knee (German Knecht, Knie) have a silent k (and used to have a c: Old English cnēo, cniht). English stopped allowing initial kn– in its words in the Middle Ages. Words imported into English from other languages tend to abide by the pronunciation constraints (phonotactics) of native English words.

So the initial /kn/ pronunciation was simplified in cnidarian, just as we don’t pronounce p-sychology or k-xenophobia with their initial consonants.