Admin blocking promotional testing

I’ll try and keep it to the point and not a rant as it’s a sore subject. But I am on a technical rescue truck in a medium sized suburban department and we have promotional testing coming up. I as well as another firefighter have put in to promote but have been told by administration that we can’t test due to there not being anyone experienced enough to replace us on the rescue.

There is no policy or anything written down stating that we cannot test, and we meet and/or exceed the qualifications to promote.

Just want some advice and/or some thoughts from anyone that has ever been in a similar scenario. We have a meeting with admin personnel coming up in a few days.