Scenario 1
The woman and the man expect their happiness in marriage to stay around 5/10.
After five years of divorce they have recovered a bit, but the woman recovers more and is now 6/10 but the man is 4/10.
Scenario 2
An alternative is that even though they are both 5/10 in happiness to start with, the woman's expected future happiness in the marriage after five years is only 3/10 while the man's is still 5/10.
Suppose they divorce and both recover the same to 4/10 after five years.
Analysis
In both scenarios after five years the woman will be happier if she divorces, and it may make sense for her to file for divorce depending on her risk tolerance.
Woman filing for divorce more could be evidence for scenario 1, which is my interpretation of your post. It could also be evidence for scenario 2, which is incompatible with your interpretation. It is not so simple to say that more filing is evidence for a better recovery for women.