They are mushy, touchy-feely places which either provide inadequate help to students overall or provide unfair help to some students over others. If you've worked in a writing center for any length of time at all, you've probably heard several of these positions before. If you haven't heard them yet, you'll hear them eventually, and if you've heard them before, you'll hear them again. Some of these arguments are completely absurd, and some of them are self-contradictory, but that's never stopped people from believing them regardless. Writing centers are unethical because the tutors who work there write the students' papers for them.
Writing centers are unethical because they undermine instructors' goals.
Teachers give writing assignments to evaluate individual student learning and progress. Assistance from a writing center tutor problematizes that kind of assessment. Writing centers are unethical because they short-circuit a student's learning process. Even if tutors don't write the students' papers for them, the help tutors provide gives students quick, easy answers to problems that the students should be solving themselves. This gives an unfair advantage to the students who use the center.