Ethos: when I am given homework, I use the Internet or other forms of help that make the work not completely my own. If I can admit that, it is probably true for most of my students as well.
Pathos: does anyone actually enjoydoing homework? How often is success built upon enjoyment? How often is failure built upon disinterest?
Logos: if classtime is used properly, there is enough time in the day to include review, a new concept, and independent practice during school time.
One could also argue that a student who understands and grasps a concept does not need the extra practice homework is intended to provide. We could logically show that once a student understands a concept more practice is not necessary. He/she will not gain from extra work. Of course, I do not necessarily agree with this argument. There are certainly plenty of counter arguments against it. However, it is a logical statement to claim that once a subject is mastered, further practice will not improve understanding since the student's understanding is already complete.
I agree with Post 3 that homework is often necesssary and beneficial. If I were forced to try to argue against homework from a logical point of view, I might claim that sometimes it is excessive, sometimes it is indeed busywork, and sometimes it kills the interests of students in studying and learning. I would try to make a logical argumentagainst excess. That, I think, is an argument that might actually be persuasive to many people.
Actually, the above depends on the (false) factual (not logical -- there is a difference) assumption that one can learn entire fields of intellectual inquiry in a few hours in a classroom with no need to work through problem sets or vocabulary or write essays on one's own.
The questioner probably should attempt arguments from pathos -- the poor overworked student, struggling over the light of a single candle in a freezing garrett, until the wee hours of the morning, at the sacrifice of her own health, to complete the homework with great diligence even at the expense of health ...
Of course, realistically, such arguments are nonsense, and in most fields knowledge comes with immersion and practice. You don't learn math without doing lots of problems or Latin without memorizing verbs. Thus homework is important, and if it means cutting back on Facebook, video games, etc., all to the good.
From a logos standpoint, I would say that students should not have to do homework because it does not really teach them much. The homework that is given is often brainless busy work that does not have any real benefit. This is a logical argument -- homework has no educational value so it should not be assigned.
Because homework is difficult and very dull.
From ethos and logos point of view, I am in the favour of some special type of homework that can improve their skills without taxing the time of other students in the classroom. I have some students who have very poor writing that is at times illegible. They can be taught in the classroom how to write various alphabets but practicing it in the classroom would waste the precious time of other students. This situation warrants homework.
I personally think that practice exercises for homework make a case for logos and ethos simultaneously.