The reason Regina was the curse breaker was because the Curse still recognizes her as the ORIGINAL Curse Caster. And she had the will to break the curse or not the first time, and I think being the original caster still granted her some right in the curse.
As for Emma…I think she still could have been available to break the curse as well due to her being the ORIGINAL Savior…so Regina or Emma could have broken the curse, but in order for us to come full circle, Regina was required to break this curse. Also due to the fact that this is really between the #WickedSisters in the end.
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"If you go as far as you can see...you will then see enough to go even further." - Finn Balor