The Buck stops here.
I once had the opportunity to observe a pretty cool Capt handle a disagreement with our dispatcher. Capt was requesting a change the dispatcher felt wasn't warranted. So, the Capt finally acquiesced---then asked the dispatcher what hotel he should plan on going to? Dispatcher puzzled, asked What do you Mean? Capt replied that it's a joint responsibility and we are at an impasse, so since the plane's not moving until we both agree, I naturally assumed you were going to replace me with a different Capt who might agree with you. The Buck stopped there, no ranting-no raving-just a calm cool discussion of who was ultimately responsible for operating the plane.
Personally, I would be ashamed to be the Capt or Instructor grasping at equipment malfunctions to explain why I let the airplane slow so drastically.