The reason we don't allow soldiers to strike isn't because giving them better working conditions, benefits or compensation would threaten national security (it would merely be more expensive), but because not having soldiers available 100% of the time would be a threat to national security. We don't need the same availability from teachers.
Mr. Spock would've immediately made this distinction. He also would've objected to the whole "teachers union -> bad education -> bad economy -> bad military" handwave. I like Dilbert, but as I've said before this is why Scott is writing cartoons and not proofs.