In complement to the other answers, from How do comments work?:
How do comments work?
Comments exist so that users can talk about questions and answers without posting new answers that do not actually answer their parent questions. Comments are often used to ask for clarification on, suggest corrections to and provide meta-information about posts.
Comments are intentionally short, having maximum length of 600 characters, and allow only limited markup. URLs in comments automatically become hyperlinks. Each user may post only one comment every 15 seconds.
Comments are disposable: unlike posts, there's no revision history, and they can be deleted without warning by their authors, by moderators, and in response to flags.
When should comments be deleted?
Comments are temporary "Post-It" notes left on a question or answer. You should not expect them to be around forever: Once a clarification has been made, an edit added to the post to include new information, or the issue in the comment is otherwise resolved, it is subject to deletion. In reality, many obsolete or chatty comments remain untouched due to the high volume of comments posted, but this does not mean that they can't or shouldn't be deleted in the future.
In the case mentioned here, the comments were not made to ask for a clarification or suggest a correction, but to ask a new question, quite different (the original question is on acknowledgment, the comment asks about top journals). Hence, the comment should be deleted, and the conversation should be made in the chat, or a new question should be asked (although I would suspect that the corresponding question would likely be closed, due to its opinion-based form). Note that the search does not work on comments, making this information basically inaccessible to other users interested in the topic. Either this information is useful for many users, and should be converted into accessible content, or it is not, in which case it should be deleted.
Hence, the proper form of communication on this site should have been:
just-learning should have a left comment to
Pete L. Clark asking to join a chat conversation to discuss about the top journals, and this comment should have been deleted once the conversation had started.
There has been some discussions on the past on the possibility of contacting directly another user (Contacting/Referring to another member of SE outside of a comment thread), and this has been declined, for the reason that Stack Exchange is by design avoiding social networking features.
Now, we can discuss about what should be StackExchange, and how we can improve it, and perhaps in this particular case, it could have been useful to have an option to automatically turn the conversation into a new chat room, instead of just deleting the comments. Perhaps it could have been smoother to first leave a message indicating that the comments are off-topic, and to delete then only when another solution has been found. But in the end, deleting them was the right decision with regards to the site.
On a side-note, I personally find particularly non-constructive the attitude "if this is the way it works, I will stop contributing". No user is forced to contribute, and no user gains from contribution, apart from the collective gain of getting great answers to great questions. It is perfectly fine to question decisions made by mods, and to offer new solutions to solve problems, but someone threatening to stop contributing if they don't get it the way they want is not helpful.