The Mishna tells us that the two happiest days of the year were Yom Kippur and 15 Av. Let’s put aside 15 Av for now and focus on Yom Kippur. Why was it one of the happiest days? The gemara explains because it is the day of slicha and kapprah. Slicha and kapparah is a reason to rejoice; we should be dancing on Yom Kippur like on Simchas Torah! Contrast that with R’ Akiva’s reaction to our pasuk of “v’Hashem yislach lah.” You would think that this woman who narrowly escaped doing an aveira and is promised slicha v’kaprah should be rejoicing, yet R’ Akiva tosses cold water all over the celebration and tells us that she should be quaking in her boots, kal v’chomer someone who really sins.
Perhaps there is no contradiction here, but two sides of the same coin. The celebration of slicha and kapprah stems davka from the appreciation of just how precarious the situation one who needs slicha is in.