one may send an article to a journal and the journal accepted it. However, the author do not want to publish his article on this journal for some reason and as soon as the author get message from the journal notified to withdraw the article. Is that possible for the journal to publish after the author announced them not to publish (withdraw)?
In US (and probably many other places), unless the authors have signed a copyright transfer agreement, the journal does not have a legal right to publish the article since they do not own the copyright to the material. If the journal required the copyright transfer/assignment as part of submission process, and the authors all signed it, then the journal has the right to publish it. It would be impolite to do so after a request for retraction, but there's a difference between what's polite and what's legal.