I would phrase my counter argument strictly as cost/benefit. For $10-$30K each year, you provide a value to an average team size of 20-25 students. For the sake of argument (and nice round numbers), lets say it's $10k and 20 students. That's $500 per student. You can see how this value would increase for an aggressive team (multiple regionals, Champs, travel expenses), or increase for a smaller team.
Now, lets look at schools in general. According to
this article, schools spend anywhere from 7k-13.5k per student. That means the cost of FIRST is basically an increase in the per-student allocation of 3-7%, for those students that participate. And with all that, what do the students get? Some education that they'll be taught again when they get to college and major in engineering!
How do you put a price tag on inspiration? How do you argue what "might have been" if a team wasn't formed... would those students still have gone into engineering? Would their success in school and work have been affected?
As participants in FIRST, we all see the benefits. We can all point to specific examples of students we've seen inspired, or student's we've seen changed because of their involvement on the team. How do you generalize that, and justify the cost?