The most logical way i would go about that is to create the orange "meat" (the inner orange without the peel) first, then build a separate object that snugly fits the inner portion for the Peel.
If the Peel has no depth, which a newly created sphere object would not have if it was "Quick Sliced" in the Ediable Poly (Collapse Modifier Stack, Right Click Object-> Convert to Editable Poly, Open Modifier Panel, Select Quick SLice, and divide the Preel mesh object in a manner which you wan the "peeling of the orange" to originate)
one section of the Quick Sliced peel mesh object must then be moved with the transform move tool even 1mm, then it will be just surface geometry, making it ideal to begin the prep phase for keyframed vertex animation.
S
ince the Peel is "planar" (ie. has no depth,) collapse any modifiers in the stack, then add a "Shell" modifier and right click the "Inner Amount" Spinner to set the value to Zero, and adjust the "Outer Amount" to a realistic value. you then have a split peel with vertices that can be keyframed as you manipulate the shapes of the peel mesh object as it is pulled away from the core.
This is a rough concept and i have done animation similar to this, and you should have an easy time unpeeling the orange.
Note: If you plan on or at a point in the process of keyframing the animation, to use a modifier, make sure that "auto key" is not enabled (will highlight in red.) you should be able to use twist or bend modifiers to make it more realistic, i don't recall at the moment what modifiers would simulate the effect better, but if you know of one, then auto key must not be active or it will be locked into a keyframe and surprise you with adverse effects.
Good Luck.
