Artemis As Huntress

Is there a religious or historical reason as to why Artemis chose the role of hunting? In other cultures, it was males who took on that role. Why a female here?

Well, as I did understand the Hymn of Kallimachos, hunting seemed to be merely Artemis' hobby. Her divine task given by the Moirai was that of midwife.

And I thought the actually deity that was involved in hunting by rites was Pan, the Lord of the Forest. I thought I've read that he was promised a part of the hunted animals and that his statue even was slapped when hunters did not hunt/catch anything.

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The following I have from the article about Pan on website [You must be registered and logged in to see this link.]

"but he [Pan] was also a hunter, and hunters owed their success to him, who at the same time might prevent their being successful. (Hesych. s. v. Agreus.) In Arcadia hunters used to scourge the statue, if they hunted in vain (Theocrit. vii. 107)"