If a student wants to video a flight, I have no problem with that. It can be a valuable training aid.
However, I wouldn't be quite so hard as some of you on those CFIs who don't want the video running, at least at first. Sure there are probably CFIs who don't want to be video'd because they're awful, or they don't want documentation of them breaking the rules, or something like that. But there are probably an equal if not greater number of those who just aren't familiar with the technology and are concerned about it being distracting.
And reducing distractions is a valid concern of CFIs everywhere. Learning to fly is hard enough! Every CFI has seen it many times - the student is coming in for landing and their phone, which is mounted on the window, starts ringing or a text comes in and the student immediately looks over to see if it's important. Or their iPad on the yoke beeps or alerts about something and they immediately check it (oh, just a Facebook notification). Or it shuts down and they ignore the plane to fix the device. Lots and lots of examples of what we used to call "dropping the plane to fly the radio".
So we as CFIs see that kind of thing over and over again, and increasing in recent years. Now someone wants to bring a camera in the plane too - the first time a CFI gets that request, I think they'd be remiss if they DIDN'T step back and think about it a bit first. Sure, they've seen those youtube videos with cameras all over the place, but that sure looks distracting!
What they probably don't realize is that (at least with the GoPro I've used, and I assume others), is that it's a one-touch on and off operation and therefore CAN BE about as minimum of a distraction as it's possible to be.
So it's an education thing. Tell him you want to show him what it's like - use it on one flight. If it's too distracting, you'll stop using it, no problems.
Because they CAN be distracting! It depends on your personality. If the thing falls off the mount, are you going to try to put it back up? Maybe you won't, but some will. If you happen to notice the record light isn't on any more, are you going to try to figure out why? Again, some will, even in the middle of a critical phase of flight.
Once the CFI sees that it's a valuable training aid and you are not going to be the type to try to troubleshoot in the middle of a steep turn, I bet they will come around and embrace the idea.
