"It isn't the military - you can't chop somebody".
If a student is not progressing well, I hope that there are no instructors that will consider giving the student the chop (i.e. tell he/she to give up), as many factors have to be considered such as:-
Student/instructor relationship
Student domestic situation (may be going through a bad patch)
Instructor domestic situation (also may be going through a bad patch)
Learing style of the student
Teaching style of the instructor
Prior to becoming a full time instructor I was on the Senior Management Team heading a Human Resources Department. As a Senior Manager I had to attend many courses and undertook the Myers Briggs personality test. (I am an ISTP). It really gave me an insight as to how we all perceive things differently. As with any personality type there are strengths and weaknesses. There are some very judgemental personality types who will simply not bend and what they say goes, so if an instructor with this personality type encounters a student who they percieve to be failing they will tell them so in no uncertain terms. Is that right? Some would say so, but others with my personality profile would deal with the matter in a different way. Don't get me wrong, if I had a student who was not progressing despite my best efforts, I would see if another instructor could assist, after all the other instructor may be able to take a different approach.
In a nutshell, if someone is going to get the chop, it should not be a decision made by one instructor, all other options should be explored..