How to deal with an unreasonable reviewer asking to cite irrelevant articles?
From your answer, we can guess that you received a "major revision" decision. In that situation, your job is to modified your manuscript according to the reviewers' comments, not to try to find out who are the reviewers. Taken out of context, the comments you mention do not seem arrogant. Those comments are usual demands from reviewer, but I can't judge, not knowing your work, if they are relevant.
In that context, you deal with those comments like with any other comments:
You accept and make the changes where appropriate.
If the comments are not applicable, you explain why to the editor and let him/her judge.
It is hard to say without knowing the details of your work, but I suggest taking a step back. There are of course arrogant reviewers, but equally it could be that there are good reasons to test your methodology in further contexts. What stood out for me was:
It is rather obvious that author C is our reviewer who is asking for self-citation and threatens to reject our work on no scientific basis (Our computational methodology was well established, robustly proved, highly cited and widely used)
It sounds like your work is empirical, is that correct? In which case your methodology cannot be robustly proven, only supported or disproven. I think that's what the reviewer is getting at; they want to see you try and disprove your work in further contexts. Take the following quote:
Furthermore though the computational method is validated against work of author D, I believe authors should at least try to validate their procedure with works of
You suggest your methodology is well established, but it seems like the reviewer is trying to, again, ask you to test whatever is novel about what you have done in further contexts.
It is challenging to say for sure, especially as we do not know which work the reviewer is citing (nor much about your work). However, I think the so-called arrogant reviewer's review needs a reappraisal.
As for whether they are author C, personally, I have given reviews asking authors to cite numerous works of other authors (not myself) when the paper has made an alarming omission.
Other answers suggest you should try to assume that the reviewer is well-minded and act accordingly. This is definitely the null hypothesis.
But if you - after a good night's sleep - have still the strong impression that the reviewer just does not like your method and wants you use/cite his method, you should think about withdrawing and going to another journal
This does not mean that a major revision is not necessary - but your chances may be higher with a fresh set of reviewers.