What is the meaning of "inter" at the beginning of verbs?

At first glance, it would seem that the prefix “inter” would signify “between” (interea), as it does in the following verbs:

-intercedere - to intervene
-interponere - to insert
-interesse - to be between
-interpellere - to interupt

However, there are also a number of verbs that have the “inter” prefix that have a meaning somehow related to death and destruction:

-interemere - to kill
-interire - to die (but literally this is “to go between”??)
-interficere - to destroy

What is the prefix “inter” doing in these verbs? How is ‘between’ related to death or destruction? Is this simply a coincidence? Or am I missing something?

Lewis and Short’s definition of interimo suggests that in this word “inter” has its usual meaning of “among” or “between”: to take out of the midst, to take away, do away with, abolish; to destroy, slay, kill.

In their entry for inter, Lewis and Short list “intereo” and “interficio” as examples of “inter” meaning “under, down, to the bottom”. But in their entries for these two verbs they seem to abandon that idea.

Under intereo their definition has “inter-” meaning “among”: to go among several things, so as no longer to be perceived. From that definition it’s an easy leap to “to be lost”, “to perish”, etc.

And their entry for interficio suggests a logical transition from “to put between” to “to devour” (to put between jaws?), “to destroy”, and “to slay”.

Posted in the wrong place.
Perperàm huè missum.

One thing to keep in mind is that human languages don’t work like computer programming languages. Sometimes compound verbs have meanings that don’t seem to make sense if you pull them apart and add up the meaning like a math equation. Language is much more subtle than that. It is helpful to notice that compound verbs are “prep + verb”, but don’t get too stuck on the ideal of “interficere” = “inter + facere”. Rather, think of it as an idiom. Consider the English compound “outdo”. For someone learning English, it may not seem to have the exact meaning of “out + do”. Languages are not perfectly systematic.