This is to try to explain why some comments (posted underneath answers) are permitted, while others are not; and why some "discussions" or "debates" are permitted, and others are not.
Comments are difficult. Comments can help clarify an answer (which is good); but long discussions distract from the answers; and criticisms can become impolite and controversial (which is bad).
Comments are officially described in the Help Center topic Comment Everywhere -- which includes subjects like, "When should I comment?", and, "When shouldn't I comment?".
There's also A guide to moderating comments -- which is more detailed, and which explains how Stack Exchange thinks comments ought to be moderated.
Stack Exchange permits comments but doesn't encourage them. Commenting is a privilege (for experienced users). Comments can be troublesome for moderators (and require moderation).
Several types of comment
I think there are several types of comment, i.e. questions, suggestions, criticism, etc.
And I think that the best (i.e. the politest, most constructive, most inoffensive) form of comment are "questions" and "suggestions" -- usually better than "criticism".
Questions -- a question is a comment like:
- I didn't understand X?
- What did you mean when you wrote Y?
- Can you give a reference for that quote?
The proper response to a question might be:
- Post a comment to answer the question
- Or (especially if the answer is long), edit the answer to answer the question
- Or just ignore the question (don't answer it)
Suggestions -- a suggestion is a comment like:
- I think this answer would be improved if you explained X
The proper response to a suggestion might be:
- Edit the answer to include the suggestions
- Or just ignore the suggestion
Criticism -- a criticism is a comment like:
- I think this answer is wrong because X
- I think this doesn't answer the OP's question which was about Y
The proper response to a criticism might be:
- Edit the answer to improve it
- Or just ignore the criticism
Note that the Help Center says,
"Leave constructive criticism that guides the author in improving the post"
A comment like "You're wrong as usual" is obviously not "constructive"; and it's not about the post either (instead it's a comment about the person, which you probably never should).
Thanks, and Chat -- these are comments like, "Great answer!", and, "That reminds me of X!".
How to respond to a comment
If someone posts a comment under your answer:
- You may want to edit your answer to address the comment
- You're not required to edit your answer1, and you may ignore the comment
- Maybe you should ignore the comment, unless you can see how to use the comment to improve your answer
- You may flag the comment as unwanted (e.g. "rude", "obsolete", or something else) for a moderator to delete
1 (except, very rarely, if the comment is phrased as a command by a moderator)
Several types of discussion
"Discussion" -- you can discuss a comment (by posting another comment in reply)
"Extended discussion" -- a discussion is on-topic (and might be seen as a helpful addition to an answer) if it's talking about the answer to the question; but discussion is "off-topic" or "extended" if it's talking about something else that's not directly related to the answer and the OP's question.
Some "Extended" discussion is tolerated (it's even welcome, if it's useful and is being enjoyed by all participants) but may be moved to a chat room.
Please remember that the main purpose of Stack Exchange is to answer the OP's question. If your discussion or argument isn't interesting to the original question, and interesting to the OP who asked the original question, you probably shouldn't be posting such comments.
"Arguments" -- comments such as, "you're wrong!"2, and so on aren't really welcome or useful. If you only "argue", rather than "discuss" or "question", then it's probably better to stop posting.
2see also Can you keep "you" out of hostile comments? for example
How to post criticism
IMO the best (i.e. the politest, most constructive, most inoffensive) form of comment are "questions" and "suggestions" -- usually better than "criticism".
But a permitted form of criticism or argument is like this -- i.e. very short:
- Someone posts an answer
- You post one comment as criticism, which says "I think this answer is wrong for reason X"
- The person who wrote the answer may (or may not) post a reply to your comment
You don't post again (in reply to their comment) -- because that would be an argument, and you already said what you thought was necessary (about the answer) in your first comment
N.B. that (because you don't reply to the comment) the author of the answer is allowed to have the "last word". If you want to have the last word, then post a separate answer of your own.
I haven't mentioned that any comment and all discussion should try to be polite -- I hope that goes without saying. If you feel you should criticise an answer, I draw a line between criticising the answer (on-topic, permitted, but in small doses only like a single comment) and criticising the person (which is usually off-topic, and may be offensive even small doses).