The Spanish correr, “to run,” comes from the Latin for the same: currere.
In a “It’s not obvious until you realize it, then it’s completely obvious moment!”, this is related to the English: current.
Although current obviously does not share the same literal meaning of running, conceptually it is very similar: what is happening right now is what is running or flowing by.
So time doesn’t fly; it flows past, right now — literally.
Not to mention, think of the way they always talk about electricity: the running current.