7 years ago, a mouse experiment was performed, and samples are still available for further analysis. This mouse experiment is already published with a certain readout. Now, we publish a whole different story, and one supplemental figure stems from the samples of that old experiment, with a new analysis. The new analysis was not performed by the experimenter of the mouse experiment 7 yrs ago. Still the experimenter is a co-author on the new manuscript. Is that valid? I always thought in such a case the paper should be cited in which that experiment was performed, and then of course the person who did the new analysis on the old samples should get co-authorship. But not the experimenter, since credits for performing that experiment were already gained in the other publication?
Data reuse is the norm in several fields and encouraged to replicate results and build on findings. Many journals require that data be made publicly available upon publication. It may also be a funding requirement. If all you are doing is reusing data from a previously published work, it would seem surprising that co-authorship could be expected.
Nature Data is an example of a journal whose sole purpose is the reuse of data. Obviously, co-authorship cannot be demanded from reusing data published here. In addition this stack academia question asks about co-authorship for data reuse with helpful responses with regards funding and data availability.
Whilst @markvs answer is both true and incredibly quotable, I would say building on or completing the unpublished work of somebody is not the same as building on their published work. In the first case, co-authorship would seem entirely fair; whilst citation would seem most fair in the second case.
However, I ultimately agree with what various people have said: it isn't worth getting into a fight over. It may be better to just get the PhD and use this as an 'annoying supervisor' story to swap with other academics. To paraphrase a great expression, 'annoying supervisor' stories are not milk: they have no-expiration date.
While I think that authorship is not warranted in this case, you would be wise to submit (meekly) to your supervisor. The answer of Peter Jansson suggests why authorship is unlikely warranted.
But fighting with your supervisor over one paper isn't worth the pain it can cause if it spoils a relationship that you need to get your career started. There will be other, future, papers provided that you don't get sabotaged by a vindictive supervisor who seems to be exploiting students for an external friendship.
Protect your own long term interests. Live to fight another day. Sorry to have to say these things, but students have little recourse to such abuse.
I agree that this is a bit of a gray area. By the strictest definitions, it's quite possible they do not qualify for authorship. However, your supervisor thinks they do, and it really doesn't cost you anything to include them.
I also think you're likely underselling the contributions of the person who performed these experiments. Collecting data is...well, hard. Even when you are using well-reported basic techniques that seem to be used in labs everywhere, there is a lot of effort to bring any technique "in-house".
The person performing the experiments 7 years ago likely shaped how the data was recorded, the specific procedures undertaken, the choice of reagents and other materials. They may have made your entire project much easier than you realize. In a casual survey of other graduate students in biology, most of us agreed that all the data in our theses, collected over typically 5-6 years, probably could have been done in just 6 months if we had known what we were doing from the start. The other 4-5 years was just figuring it out and working out the kinks. All these things can be thought of as intellectual contributions that don't see the immediate link to your current paper, but your supervisor does. Just citing the older paper doesn't entirely capture the weight of these contributions. It's quite different if their work was done in another lab, and you're citing their overall methodology but still needing to do the work to replicate it in a different lab.
Authorship guidelines typically require authors to have some other contributions, though, besides just collecting data. At a minimum, they are expected to review and approve the final manuscript. My overall advice is that you should insist that they do this added step to be included as an author, rather than arguing they should not be an author by not providing them this opportunity.
It's also worth recognizing that in biology, there is no dilution of your work by including other authors. Often, the middle authors on a paper have made very minor contributions to the final work, limited to one figure of the paper, one verification step in the methods, etc, but nonetheless the paper would be incomplete without their addition. Having one more middle author will not reduce the "credit" you get for publishing the paper as first author.
One way to view this issue is to apply the "Vancouver rules" (e.g. as described by the ICMJE, International Committee of Medical Journal Editors. These recommendations outline what is required to become a co-author on a scientific manuscript. Note the "AND" in the list of requirements. It is clear that not all agree with these recommendations but it is also clear that authorship is given for the wrong reasons in many cases. In your case the authorship could be considered a "honorary or guest authorship" (COPE, Council of Scientific Editors) but would be perfectly normal if the person(s) fulfil(s) the expectations of an author, i.e. provides some intellectual input to the work to be published.
So in the end the case may seem clear but not easy to resolve if co-authors do not agree on the rules.
recontextualizing the problem
Let's say there are three researchers, Alice, Bob and, Carol. Bob and Carol each design experiments about how a treatment affects mice. They are looking at two aspects of the same treatment, so the control and treatment groups are the same. Bob's experiment uses lung tissue, and Carol's uses brain tissue. Alice is an expert in running this treatment protocol, so she deals with the mice and collects all of the tissue samples. She gives the appropriate samples to Bob and Carol and lets them take over from there.
Bob and Carol each do the rest of their experiments totally on their own with no collaboration from anyone (even each other). Then each writes a paper. At this point I think most people would argue that Alice deserves to be a co-author on both papers, due to her direct contribution. It doesn't matter if the samples Alice collected sat in a freezer one night or one week or one year. Alice's work was instrumental to Bob and Carol completing their experiments.
In another scenario Bob doesn't exist. Anything Bob would have done, Alice did. Most people would argue that Alice still gets to be a co-author on Carol's paper, due to her direct contribution. If those samples Alice collected didn't exist, Carol couldn't have gotten started.
Different fields have different standards of authorship, and different individuals have different ideas of how one meets those standards. People disagree about these things all the time. In this case I think it helps to look at things from Alice's perspective. In my own work I tend to err on the side of inclusivity, when disagreements arise. In the end it will make no difference to your career if you are first author on a paper with five co-authors or a paper with six.
If you are feeling pressure to include the original author as an author of your paper and you are considering going along with it, one way to handle the ethics is to actually reach out to that author for collaboration. If they provide even a minor academic contribution (i.e. other than assistance that is purely clerical or administrative), you may be ethically obligated to include them as an author.