ORIGINAL: piper_chuck
In addition, being an instructor and having a responsibility to protect the student's plane from the student's mistakes is challening enough with a trainer. Most are not willing to accept the additional risk, and stress, created by trying to teach with a warbird.
As an instructor I've had students show up with all different kinds of planes to learn on, ranging from warbirds to one who showed up with a seaplane (he thought that would make it easier to take off from the grass). I have never taught any of those how to fly. I send them back to get a trainer plane to learn to fly on. Why?? It's just like Piper_chuck said, it's hard on an instructor to teach different planes like that. When using a trainer it can be all an instructor can do to keep them from crashing, I'm not going to complicate that for myself by adding in a plane like a warbird that is more difficult to fly in the first place.
On a similar note, we have a guy at our field right now that "refuses" to buy a trainer. He doesn't want to "look" like a beginner flying with a trainer. Right now he's trying to learn flying a 4-star 60 with an instructor (not me, I refused to teach him unless he got a trainer). While he is learning to fly, he could learn a lot faster with a trainer instead of the 4-star. But I just don't understand that kind of attitude. Heck, we've all been there when we started, we all owned trainers. But anyway, the point I am trying to make is that sometimes it's up to the instructor to play the bad guy and tell the student that they just can't learn to fly on what they have brought out. If the instructor doesn't say that to the student then he is doing a disservice to that student by not setting them straight.
Ken