Please help resolve the following challenge: I have two feature classes, which have the same number of polygon features, that when overlaid form concentric "rings." I need to erase the inner circle from the outer circle for each feature, matching them by their record ID. So, if both feature classes 1 and 2 have records A, B, and C, I want to erase the polygon of Record A in FC2 from Record A in FC1, RecordB in FC2 from Record B in FC1, etc.

ArcGIS' Erase function will only take the entirety of the feature class and erase from them - I can't find a way to link up records by their feature ID.

Any suggestions are very much appreciated. I'm working with Arc10.1 with all licenses.