Questions says it all. Why do we call it "breaking in" when we refer to relaxing the stiffness of worn objects/tools? This use of break is similar to the "breaking the spirit" or a wild animal. But otherwise it doesn't follow from the regular mean of break, which implies the object will no longer function. In this case, the function of the object is improved.
Learn English – the origin of “Breaking in” as in a shoe or glove
etymology
Best Answer
I think it probably is an extension of the earlier transitive usage of “break in” meaning teaching or training someone to do a new job, on the notion of “training” your new shoes till they become more confortable.
Break in :
(AHD)
The expression appears to be from the second half of the 19th century; the earliest example I could find is from a 1867 edition of "A Japanese and English Dictionary"