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I submitted the preprint to arXiv and the manuscript to a Physical Review journal, and someone asked me to cite their article after seeing it from arXiv.
Their paper is a review. After reading that paper, I find that it has only a weak connection with our work.
My supervisor asks me to cite it. Should I refuse to cite?
I can think of a number of reasons to cite a source:
"Being asked" is not among them.
Unless you retrospectively find that one of the reasons above applies (esp. 3-5), politely decline to cite the paper in question. In particular, you should refuse to add a citation as a favor.
Addendum: I just saw your update to the question, stating that your supervisor asks you to cite the apparently irrelevant paper. This complicates the issue. I would ask them to explain why and where to add the citation. Perhaps they want you to slightly revise your paper, incorporating information from the new source, which would justify the citation. If not, it depends on your relationship whether you are in a position to push back.
I will just share my experiences (bad ones) to throw in some perspective.
I had submitted a paper once to a top conference in computer vision which was rejected for good reasons acceptable by me. But one of the reviewers, which I guessed was a top name in that area (also had a coursera course), asked me to cite 5 of his papers in the review. All were his papers.
A few years later, when I am doing my PhD, I got a paper accepted in a top conference. This time my supervisor sent me a list of 8-10 papers which I had to cite. Since there were constraints of space, he asked me to truncate a diagram and reduce the size of images to accommodate his list. Those papers had no relation whatsoever to my work. My supervisor is an IEEE fellow and has more than $1M in grants.
Citations improve H-index. H-index is crucial to get promotions and fundings. We had a very highly talented lecturer joining our university. He got 3 ICML papers accepted as first author (a top conference in machine learning) within a year, which is a fantastic achievement, but his grant application was rejected in favour of another lecturer who had 20 papers in mediocre conferences but a much better H-index. She works closely with my supervisor-- is a part of his nexus. The lecturer left my university and joined Google.
Academia is rotten with such practices. I regret that I agreed to add those citations - should have fought back. But then, fighting back is of little consequence when the system is fundamentally broken.
Should I refuse to cite?
Do nothing. You've read the paper and found it "has only a weak connection with ours," so there's no need to cite. You needn't refuse; just do nothing. If you must respond, then say something like:
Thank you for bringing your work to my attention. I have taken a look, but I don't see a strong connection and as such I believe it would be inappropriate to cite. If I've missed something, do let me know.
You can add a comma to the opening sentence and follow with I found it interesting, if appropriate.
Politics! Politics! Politics!
If you didn't read the review paper and went direct to the original paper(s), I can't see why you should cite a secondary source. If you did that exhaustively, you would include everyone's textbook about the subject plus the Wikipedia entry!
Alternatively, if there is pressure, look for one or or more specifics where the reviewer has thrown light where you would or could have missed it. Or maybe give a cursory acknowledgement by simply saying, "There have been a number of useful review papers in this area including X, Y and Z." and say no more.
