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.