Dr. Primrose explains to Olivia that in human endeavors a small evil is allowable if it leads to a greater good - like lopping off a leg to save a life. BUT, in RELIGIOUS matters, evil is NEVER allowed...no matter how small or for what good purpose.

The reasoning is that if you PURPOSELY do the little evil thing to bring about the greater good thing, you are STILL GUILTY of the sin from that little evil thing. Eventually, (whether an hour later or a year later or whenever) the good thing will come about because of the little evil thing you did. THEN your sin from that little evil thing would be forgiven. BUT...if you DIED before the good could come about from your little evil sin, you would die with the sin on your soul.

Therefore, Olivia cannot commit the little evil of breaking her vow of secrecy on the priest's identity. If she informs on him to the authorities and then SHE dies before he is brought to justice, she will have died with the sin of 'breaking a vow' on her soul.