The old man said that the snake would die if it was slightly injured, because it would not shed its skin. Is that so? Isn't it true that a snake will not die if it is cut in two?

"I can't peel it and die" and "I can't die if I cut it in half" are two things that are not closely related.

Cutting it in half won't kill you immediately, but it will kill you if you hurt your internal organs! Of course, it is also possible not to be infected after removing the tail.

A snake won't die with a little skin injury. Snakes are often injured in the wild. If you bleed and run away, you can live well and not be infected. Snakes have to shed their skin, and they can't shed their skin just because of a little injury.