I think the answer to your question is because the parents/students want it so. I looked for some numbers of how many families wanted JROTC as a P.E. credit course and how many did not, but could not find any. The best I could find to support my initial assessment is the article cut and pasted below.
According to the article parents, students, and teachers are in favor of the JROTC; I would wager for the same reason I am, discipline and good training. Perhaps they do not feel the same way about the other student activities you mention.
The Voice Of Asian America
Save JROTC In The San Francisco Schools
By: Nelson Lum, Jun 16, 2008
In November 2006, the commissioners of San Francisco's Board of Education attempted to eliminate the popular Junior Reserve Officers Training Corp program from the city's high schools. The resolution directed the program to be phrased out in two years and called for the creation of a task force to find a comparable replacement program. It passed despite overwhelming opposition from parents and students. Since then, the task force has not been able to find anything that can compare favorably with JROTC, and last December, the commissioners, by a 5 to 2 vote, extended the program until June 2009.
JROTC is a program supported by all principals of the affected schools, all alumni associations, all parents and teachers associations, and all student body associations. Asians comprise more than 70 percent of the program, and minorities comprise 90 percent. It requires participants to perform community services and is strictly voluntary. In 2007, JROTC cadet seniors had a 100 percent graduation rate, while their non-JROTC counterparts had a rate of approximately 90 percent. Commissioner Eric Mar, who voted to eliminate and to not extend the program, has consistently praised the program for its effectiveness in developing leadership, discipline and character for the cadets.
Mar has stated many times that his main objection to the program is his belief that it is being used as a recruitment tool for the military. A closer look at the facts simply does not support Commissioner Mar's contention.
At the end of the 2007 school year, only two out of 1,465 cadets in the JROTC program enlisted in the military. The percentage of enlistment into the military by non-JROTC students was and has been higher than JROTC cadets. In fact, JROTC's policy prohibits instructors from recruiting.
As we all know, the school district is experiencing a budget crisis. Half of the JROTC instructors' salary is subsidized by the federal government (approximately $586,000 for 2007), which also pays for all instructional materials such as computers and uniforms. If this program is eliminated, additional teachers will have to be hired at full cost, something the district does not have funding for.
It would be detrimental - both fiscally and socially - to the schools if this program was eliminated. JROTC has proven to help students develop leadership skills, discipline, assertiveness and, most importantly, self-esteem. High schools must find ways to facilitate these young men and women who, had they not found a social group to belong to, would likely have experienced a negative affect on their social development.
A group of parents, educators, veterans and concerned citizens formed a committee to fight for the reinstatement of this program. They recognize the value of JROTC for our youngsters and are aware that, if the program is eliminated, San Francisco will most likely never be able to reintroduce it again. There are currently over 700 school districts on the waiting list for JROTC. San Franciscans should feel fortunate that this program is established in their school district and available to their students. The members of the committee have chosen "Choice for Students" as their slogan to get a ballot measure for the November 2008 election, so all San Franciscans can make their voices heard.
Choice should be offered to students and their parents. San Franciscans just passed Prop A to support their schools and students, and should continue fighting for better schools and more programs for their students. The committee welcomes and needs everyone's help.