How to respectfully challenge advice My question is regarding how to go against advice given by advisers/faculty in a professional way, specifically in applying to graduate schools (but I am interested in the general case as well). Due to my poor test scores, one of my mentors has explicitly said that I should not apply to school X and Y. However, the location of the school and research interests of the faculty align well with my preferences so I want to apply anyways (although I must agree with my adviser that my chances are slim at best). How should I let my adviser know (he is likely to be a letter-writer for me as well)?

On a related note, should I follow his advice? I don't want to "waste" time applying to a school that is a big reach for me but I also don't want to lose hope.
For the general question: One answer lies in the question itself. Challenge the advice with respect to the advice and your advisor. That is, appreciate and acknowledge the experience of your advisor (not necessarily in words, but at least "internally"). 

Moreover, give some reason. "Thanks for your advice on the topic, but I would like to do...  because..." I feel like "I'd like to do it anyways" is not the best reason...