When the members of an all-girl robotics team from western Afghanistan learned that they were going to participate in the inaugural First Global Challenge — an international competition that will be held in the District of Columbia this month — they traveled 500 miles to visit the U.S. Embassy in Kabul.

The six teenagers risked this arduous journey not once but twice, hoping to secure one-week business travel visas to the United States.

Their efforts ended in tears when their visa applications were denied. Now, they will watch from afar as their robot competes without them.

This is a dispiriting — and, for the United States, self-defeating — end to what might have been an inspirational story. The team faced long odds, not least because they were girls striving for a technology-based education in Afghanistan.

According to a recent Thomson Reuters Foundation expert poll, the country is the most dangerous in the world for women. Girls have been threatened with grenades and acid attacks for attending school, and 55 percent of school-age girls are currently missing out on an education. Science and engineering are especially male-dominated, making the team’s achievements even more striking.

The Afghan girls also faced unique challenges when trying to assemble their robot. While other teams received their materials in March, the box sent to Afghanistan was held up amid terrorism concerns. Yet the girls remained undaunted and began building prototypes with household supplies.

As one member of the team told Forbes, they just wanted a chance to prove themselves to the world. How sad that the U.S. government has prevented them from doing so in person.

These girls embody the values the United States has championed around the world and sought, at great cost, to cultivate in Afghanistan. Their story is a testament to innovation, entrepreneurship, equality and grit. Given that the U.S. government has also invested substantially in promoting girls’ education and women’s empowerment in Afghanistan, the visa denial is inexplicable. (And, in fact, the U.S. government offered no explanation.)

Though few business travel visas are granted to Afghans each month, it is hard to understand why the State Department would not make an exception for these intrepid girls and all that they stand for.

In their mission statement for the competition, the girls wrote: “We want to make a difference and most breakthroughs in science, technology, and other industries normally start with the dream of a child to do something great. We want to be that child and pursue our dreams to make a difference in people’s lives.”

We can only hope that their dreams, and the dreams of other Afghan students, are not extinguished by the State Department’s perplexing decision.