The military responds that it does so because graduates from regular high schools are more likely to stay for their entire three year enlistment. The article quotes a Pentagon spokeswoman as saying:
Data collected since 1988 shows only 28 percent of graduates with traditional diplomas leave military service before their first three years in uniform, while those with non-traditional backgrounds have a 39 percent attrition rate. (snip) It comes down to money because its costs $45,000 to replace someone who hasn't met their full term.
Clearly, some portion of kids who go to "alternative" high schools have difficulty "fitting in" to the regimentation of regular high schools. "Regiment" is the root word of "regimentation."
Having difficulty doing what you're told doesn't work in the service. Hence the 11 percent greater drop out rate for non-traditional high schoolers.