Background: There was an answer on one question that referenced a personal anecdote of physical punishment. I argued against that answer, at first pointing out the fact that it was anecdotal. A discussion about this ensued between me and the answer's author in the comments, which I considered to be constructive, proceeding and civil from all sides, even though clearly adversary.
The poster of that question reported that admins removed all the discussion defending the anwser, and left only one comment, critical to answer, the in the comment section. The answer's poster, quite understandably, removed his answer thinking it the site prejudiced against his position.
My question is: Is discussion about an answer something we should discourage on this site, even to a point where it gets deleted?
If not, what would be the proper way to deal with an answer that argues something I think is incorrect? Downvote without explanation? Downvote with explanation, but without the poster being allowed to argue back? Downvote with explanation, with the poster allowed to argue back, but the downvoter not allowed to reply?
Or would downvoting an answer I disagree with because it is based on false assumptions even be appropriate, if the answer is otherwise well constructed? I don't personally think so, I'd reserve downvoting for simply poor or inappropriate answers.
One part of the problem may be that a criticizing comment (which I think everyone agrees should be ok) will lead to making the answer better if the answer's poster agrees (or doesn't do anything about it), but in case he disagrees, that same comment isn't a just criticizing comment anymore, but the first comment of a discussion.
And how are we to correct anyone's view if discussion about the basis of that view is not allowed? Or is that even the purpose of this site? (And there's also the related discussion on whether parenting topic is even valid for the SE format, on the basis that the topic inherently provokes discussions.)
With a site that will have controversial or otherwise discussion provoking topics both in questions and answers, this is an important issue to consider.