Given that this blog is devoted to discussing moral issues, a natural question would be, why do so? The following thoughts are not meant to be exhaustive, but they are some of the things that come to my mind.
First, in our culture people are prone to attend more to feelings about morality rather than reflective thought about morality, and this can have harmful personal, social, and political consequences. I might feel strongly that I am justified in responding in anger to what someone has said or done, but I may be wrong about this. Acting out of the emotion might damage a relationship, perhaps in deep ways. Or I might feel that something is wrong, but this could be grounded in something besides the truth. Feelings are important and perhaps contain value judgments, but they are no substitute for rational reflection. We depend too much on our guts, rather than our minds, when dealing with ethics.
Second, some of life's most interesting and important questions are moral questions--abortion, euthanasia, affirmative action, the duties of parents, the definition of true happiness, and the nature of virtue, to name a few--and if we want to live good lives as individuals and as communities, we ought to reflect on such issues in order to apply the fruit of our reflections to our lives. This is why an education (both formal and informal) in the humanities is important, as it can help us in these and other ways.
Third, while we may not reach agreement about right and wrong, we can still make progress. One important aspect of such progress occurs on the individual level. The student of ethics can make progress in understanding important issues, rather than being misled by arguments that fail upon closer inspection. Knowing that a particular argument is unsound is valuable, and worth the effort that justifiably drawing such a conclusion often requires. Even if others don't agree with her, she has still made progress. A lack of agreement doesn't entail that she is wrong (though it may). At any rate, this sort of progress is important, because it increases our stock of true beliefs, which is both intrinsically and instrumentally valuable. That is, having more true beliefs is good in and of itself, and it is good for helping us accomplish other things of value in life.
Finally, thinking and talking with others about moral issues is simply good fun. Or at least I think so.