if the world was a flat (i.e. 2 dimensional) 18% grey everywhere illuminated by difuse light what mode you shoot in would not matter, the camera would get it right every time
unfortunately (or perhaps fortunately) the world is not like that.
the arguments made by flyer are very true.
1) regardless of mode, if you have a consistent method of working to correct exposure without a lot of trial and error, it is a valid way to get to the end objective.
2) It is also important to, as an instructor, explain why something is done, not just do it. The teaching is not in insisting that you use manual, but expplain exactly what you are adjusting for and why. It is also to teach how the camera works, how each mode works, etc... Because you won't get the end result or even a consistent method (i.e. point 1) without it.
the same is true, and forgive me for hijacking the thread momentairly, of the raw vs jpeg debate. Learning how JPEGs are processed and optimizing the in camera function can yeild the same results as RAW, and all the arguments about using raw are really just a compensation for
NOT learning part of your camera's function. But this is not the purpose of the thread.
but, back to the purpose for the OP, making adjustments to get the end result, and whether M is the correct mode to do this.
the only thing with manual mode that is an advantage over all other modes (aside from working with Manual apature lenses where you need to) is that there is no coupling of controls, you can set each thing independant of the other, and the result is what your setup gives.
Other modes will some times give you things that go outside the bounds of what you want. In Av it can set the shutter incredibly slow, without you thinking about it. in Tv you can run out of apature range, with auto ISO it can with flash bump the ISO too hign and then use only minimum flash, etc....... it is too easy to forget all the ways some auto functions work, manual makes you think it through a little more, that is all!