Why is the mitzvah of sending away the mother bird before taking the young called שילוח הקן (Shiluach haken; "sending the nest")? It's not the nest you send away; it's the mother bird. I would have called the mitzvah something like שילוח הציפור (sending the bird) since that's what one does. Alternatively, שילוח האם (sending the mother) matches the language from the Torah: "שַׁלֵּחַ תְּשַׁלַּח אֶת-הָאֵם".
So why is the mitzvah called shiluach haken?