In addition to being a story about choices and consequences, "Tell Them Not to Kill Me!" can be examined for its theme of relationships between fathers and sons. As you plan your essay, annotate the story for exchanges between Juvencio and Justino as well as what the colonel has to say about his own father, Guadalupe Terreros.

An approach to analyzing the story could compare and contrast the relationships of the story's fathers and sons. The story raises questions about how far loyalty to family or filial devotion can reasonably be stretched, and if there is a breaking point, where it lays, in the view of the author.

If this were the approach you would take to analyze the story and write your essay, then a thesis statement could look something like this:

In "Tell The Not to Kill Me!" by Juan Rulfo, a father exhorts his son to try to save his life; at the same time, another son works to avenge his father's death many years before, suggesting that the dynamics of father and son relationships are complex and sometimes unpredictable.

If I were to write an essay or composition for this story, I would probably concentrate on the title.

The title is based on Juvenico's plea to his son to keep the police from killing him.  The problem, of course, is that Juvenico is guilty of the crime of which he has been accused: murder.

The story seems to circle around the issue that Juvenico took another man's life and has been on the run ever since, living quietly, staying out of the public eye so that he will not be caught and punished.

When he is caught, he tries to reason with the authorities that he is too old to be worth killing, and he has suffered enough feeling hunted and worried all the time.

Of course, Juvenico receives no sympathy at all from the colonel, who is the orphaned son of the man Juvenico killed.  It seems almost ridiculous for Juvenico to try to rationalize that what he has done should be forgotten now that he is old and has lived in fear: at least he has had the opportunity to get old, while Don Lupe's life was cut short over the death of one of Juvenico's animals.

My thesis, therefore, would concentrate on how each person makes choices in his/her life and must assume the consequences for those choices, rather than expecting someone to take the hit for his/her mistakes.  A person may spend many years trying to avoid responsibility, but it is generally impossible: if someone is able to avoid paying a penalty literally (physically), there is a good chance that person will pay mentally or emotionally.

We see this with Juvencio: before he is caught, he suffers by having to live half a life--always in hiding, always afraid of capture.  However, after he is caught, he now must literally pay for his crime by being executed.

This seems to be a solid thesis which can be easily supported by details from the story.