So at this point, Logan has fought in the Civil War, World War I, World War II and Vietnam. (He doesn't really age much; that happens sometimes in fantasy films.) He's been riddled with bullets on the beaches of D-Day and while charging a machine-gun nest. He's been executed by a firing squad. Despite it all, he's doing fine.
Now an official has a fresh offer: "I'm going to make you indestructible."
WHAT?!? Just what about this guy's history suggests fragility or destructibility.