What does "of the other" mean?

In Pulp Fiction (1994), Captain Koons says to Kid:

Captain Koons: See, I was a good friend of your dad’s. We were in that
Hanoi pit of hell together…over five years. Hopefully…you’ll never
have to experience this yourself, but when two men are in a situation
like me and your dad were…for as long as we were, you take on
certain responsibilities of the other. If it’d been me who’d–not made
it, Major Coolidge’d be talking right now to my son Jim. But the way
it turned out, I’m talking to you.

What does "of the other" mean?