The words "surjective" and "bijective" have transparent etymologies: "sur" is French for "on" (as in, "onto"), and "bi" hints at the two-way nature of bijective functions.
"Injective" is more of a mystery. All functions "inject" every element of their domain into the target space, and there is nothing about the word "inject" (in English) that suggests two things can't be injected into one thing. (E.g., you can be given two different injections at the same point on your arm.) Is there a sensible etymology or reason that this word came to mean "one-to-one"?