A "not full frame" carrier is not a half frame, it is just the normal carrier that covers a bit of the rebate. A full frame carrier allows a bit of the rebate to show so there will be a black line surrounding the edge (if that is what works and what you want.) Not everything works with that technique either. The image should drive the presentation.
I am one of those teachers who encourage students not to have strong white's near the edge of the print, especially for beginners who's compositional skills may not (or may ) be very sopishicated. This is because the eye is drawn to the lightest portions first, that is the way our brain works. As several others suggested in the previous comments, why have the viewer eye be drawn out and away from the image. that is not to say they should have burned in ugly grainy grays, just be careful when composing and pushing that shutter. Just as the image of Brett Weston's works, the whites do not draw the eye away from the important message of the image.
However, compositional rules are not carved in stone and if the images works, it works, regardless.
Several years ago there was a young fashion photographer, Madureen Lambray who had server blown out highligts, white edges every where; however, the images worked . Which is the bottom line. This particular instructor would have given her an F, which would have been sad.
I have a student who has been working on a series of portraits that i feel are much too contrasty. During a recent discussion about this, she comment that she admired Richard Avedon, which was a great piece of important information as to the direction she was striving to reach. So rather than to continue pushing her to "change" her vision, I said, ok , let's take his style and work see want you can do to recreate that type of image.
It is too bad that this instructor seems to be caught up in being right (read ego) rather than present options with reasons as to why; however, depending upon the images placed before me, i might say the same thing. It is also too bad that you will end the class not feeling positive about the work.