Some fabrics fray more than others. If you have pieces that really fray, you may want to "pink" the edges (use those pinking shears that cut zig zag lines) after making the seams a little larger than normal.
Some folks use their babylock machines to finish the edges as they piece.
I tend to agree with your teacher that if you zigzag the edges too heavily you may wind up putting a permanent wobble in your pieces.
Are you just worried about the cotton rubbing on the floor to cause the fraying or is there something else that could be a problem? Most of the time, the fraying stops once you put the seams in, but some materials are really not woven together well and could fray more than normal.