The gods weren't known for their small egos. Basically, if you wanted to avoid a twisted punishment from a Greek deity, you'd want to go with something like this: "Oh, I might be mildly talented, but I'm nowhere near as talented as you!"
In some versions of this myth, Actaeon dares to tell Artemis that he's just as good at hunting as she is. Oops. By saying he's better than a god, Actaeon is committing what is known as hubris to the Greeks—basically, it means you think you're better than a god. By the way, this never works out well for mortals.
Questions About Hubris
Was Artemis's reaction appropriate for the situation? Did turning Actaeon into a deer have some relation to the act of hubris he committed?
Can you think of other instances in mythology where mortals were punished for their hubris?
Based on the rest of the story, do you think it makes sense that Actaeon committed this act of hubris? Or do you think the story is more believable without that tidbit?