As for the LDS, the only thing I can say is that all organizations evolve and I see the desire for girls to be able to challenge themselves and achieve the same things that the boys have an opportunity to do (most girls could easily do all of the requirements throughout the Scouting program on the path to Eagle). Note that everything changes and there used to be a time when certain boys (non-white, non-Christian, gay, etc) were excluded from participating so opening opportunities for girls makes sense and is a natural part of a growing inclusive organization.
.