After looking on a 10 or so etymology websites and hard-copy references, I have been unable to find origins of the phrase "take it out of hide" (indeed I didn't find any reference at all to the phrase). A Google search suggests the phrase may be more common in military related documents. Older dictionaries note 'hide' having a meaning of a particular plot of land intended to be sufficient for sustenance of a family. A possible origin there, e.g., whatever the size of your brood, you don't get more land, you take it out of hide? Associates I've asked assume the origin of the phrase is somehow related to tanned animal hides, e.g., whatever you are making you have one hide.