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Negation of Advantage

At our table we use the Variant Flanking rules, however we noticed the same problem as yourself, and added the corollary that you cannot gain the advantage of a flank if you yourself are being flanked.
The thematic justification was that you are busy trying to cover your own back and can't put all of your attention onto exploiting the enemies defensive gaps.

This is justified mechanically under the rules for gaining advantage and disadvantage:

"The GM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result."