According to Wikipedia, at least for IC packages:
The dual-inline format was invented by Don Forbes, Rex Rice and Bryant Rogers at Fairchild R&D in 1964,[3] when the restricted number of leads available on circular transistor-style packages became a limitation in the use of integrated circuits.
We can guess, since this is an American company in an era long before metric dimensions became common in manufacturing, that 0.1" was an "obvious" choice.