From what I have been told, quilt binding should be "full", meaning that the batting completely fills the binding. Judges check for that, but more important the binding lasts longer and looks better if it's full.
I prefer the look of .5" binding and would use .25" only on very small wall hangings, but this is just my personal preference. I think some judges prefer thin binding. That doesn't matter to me, since I don't intend to submit any quilts for judging. As long as your method gives a full binding with consistent width, the method doesn't matter too much. You do need to select a strip width that matches your method though. I use your teacher's method with 2.5" strips, and I don't pin. I do use the walking foot, and my walking foot also allows any needle position.