Rumination is for cows. Literally it refers to the "chewing of cud" which in similar animals is necessary for the digestive process. Rumination for us implies a fixation on distressing events and thoughts and repeatedly examining them.
It is similar to worry which is more concerned with future possibilities than those of the past.
In either case the time and energy spent on neurotically re-living past failures or obsessing over future possibilities does nothing to promote health or optimism for the future.
It also robs us of the precious present moment. We literally walk past natural beauty around us, ignore acts of kindness, are oblivious to our own opportunities to relate to others, and generally exacerbate our own suffering.
Now it can be useful to examine our own lives in an effort reduce our weaknesses and help ourselves to evolve. But many cross the line. Examination becomes obsessive. We ruminate.
Rumination can lead to depression when it is allowed to fester.
So by all means examine our lives, identify mistakes for their ability to teach us how to cope in a healthier manner. Then let it go.
Rumination is for cow, not people.