Firstly, it's important to keep in mind the lofty goals and ideals of the scouting organization. According to the Boy Scouts of America, “the Scouting program has three specific objectives, commonly referred to as the "Aims of Scouting." They are character development, citizenship training, and personal fitness.” No one can make the case that girls will not be well served by a program with these aims. But my argument is not that girls will benefit from being Boy Scouts, but that the aims of scouting can only be achieved, for boys, if girls are included in the program.
Remember the era in which Boy Scouts was founded, the very early 1900's. For the most part, Women and Men had very different roles in society. Very few women, as a percentage of society, worked outside the home. The work Men performed was typically labor intensive.
Baden-Powel was a war hero who, "while stationed in India, discovered that his men did not know basic first aid or the elementary means of survival in the outdoors. Baden-Powell realized he needed to teach his men many frontier skills, so he wrote a small handbook called Aids to Scouting, which emphasized resourcefulness, adaptability, and the qualities of leadership that frontier conditions demanded." This handbook became the basis for the scouting program which was meant to prepare young men for adulthood.
The basic unit in Scouting, the Patrol, is based on the tendency of boys to naturally form neighborhood friend groups or neighborhood gangs. The thing is, these neighborhood friend groups haven't been exclusively male anytime in recent history. and mixed gender groups of friends are now the norm, just watch any Disney show.
The workplace of the early 1900's was very much segregated, but today there is no such segregation. As men, today's boys will work alongside and report to women in the workplace. If the Boy Scouts of America is to prepare boys for the challenges they face in life artificially limiting their interaction to a male-only institution is counterproductive.