Peer review of your article is perhaps the biggest test in publication. The comment of a reviewer is a critical part of the publishing process that journal editors take very seriously. Therefore, it is important that once the comments are shared with you, you respond to them both efficiently and effectively. However, there are many instances where you may mildly or even strongly disagree with the peer review comments. Such eventualities need to be dealt with very diplomatically such that both reviewer and journal editors are not offended.
Here are some tips on how best to respond to a peer reviewer on their comments:
Note 1: Irrespective of whether you agree or disagree with the peer review comments, you have to appreciate the fact that a peer has taken the effort to review your manuscript. All reviewers are fellow academicians who too are as busy as you are. For young authors, understand that some senior reputed peer of your field has actually put in the effort to evaluate your work. Therefore, it is a professional courtesy to thank them for reviewing your paper. All your responses must follow in the same vein.
Note 2: Address all comments. Acknowledge the positive comments as you address the negatives. Your response must reflect that you have thoroughly gone through the comments in totality and not just nit-picked those on which you disagree.
Note 3: Draft a response letter, which is to be separate from your edited article. Many authors make the mistake of sharing only an edited manuscript with a covering letter to journal editors. You cannot expect the reviewer to go check for themselves whether you have addressed all comments! Draft a letter in which you explain what are the changes you have done, which comments you do not agree with, or which comments you cannot address.
Note 4: It is ok to disagree with some comments about peer review. It is also possible that you may feel that the reviewer has not understood your paper properly or have completely misread it. Such comments are infuriating and it is hard to be patient about them. But do understand that the entire process of the peer review was introduced in the publishing process precisely for some expert to read manuscripts from their own knowledgeable perspective. Thus, the reviewers are considered a peer simply because they have a unique perspective and it your responsibility to communicate your thoughts effectively to them. Respond respectfully, saying why you disagree with some of the comments by explaining your thought process, where you are coming from, your approach.
Note 5: If the reviewer points out some glaring mistakes, be upfront, and apologize about it. It is often fruitless to argue on some point simply because you are too ashamed to admit it was a stupid mistake on your part! Reviewers and journal editors appreciate honesty. So, if you made an honest mistake that the reviewer points out, thank them for it and let them know you have rectified it.