In the real world, what is necessary and what is right are sometimes at odds. This seems to be the case in all such questions of including advisors/supervisors as co-authors on papers.
In mathematics, which I consider to have a sensible approach, advisors are never included (well almost never) unless they make a direct contribution to the paper. They are actually often omitted even when they do and are happy for just an acknowledgement. I think that Philosophy is like this also. Neither myself (mathematics) nor my daughter (philosophy) included advisors as co-authors. Never. Even. Considered. It.
In some lab sciences, especially, a supervisor has created the conditions under which the work can proceed and even funds lab assistants, etc, that make all work possible. In those fields it is normally considered necessary to include the supervisor as a co-author, and even as first author in some cases. I think of that as less sensible, but it is the norm.
The other answers so far given here seem to be suggesting ways to make the supervisor a real contributor to the work so that they can be rightly considered a co-author. But that isn't how the world works in those fields that traditionally include supervisors in the author list. No one, for example, caries out completely independent work at CERN on the Large Hadron Collider, for example. Lots of people participate in some way, including those who built the thing in the first place.
The solution to the dilemma here, is just to ask. But ask in person. Provide the supervisor with a near-final draft and ask "Should you be co-author of this or not". Simple and clean. There are three possible responses: (1) of course not, (2) of course, and (3) let's see....
Only 3 requires any real thought and you can work it out, depending.
I'll note that, depending on your field, it may also be either an advantage or a disadvantage to have the advisor (or anyone else) as co-author. In some fields, co-authoring a paper with a prominent researcher can boost your career, as you are seen to move in the halls of power. In other fields, where they count "chits" and "split hairs", only sole authorship (or at least "first" authorship) is valued, including the supervisor can hurt. I don't know what is the case in your field and assume you don't either or you wouldn't be asking. But your advisor certainly knows, leading to responses (1) or (2) in most cases.
But if the response is (1) you need to ack the advisor. If it is (2) it could be a career killer to refuse, since you need letters to advance. If it is (3) then the other answers here from lordy and Wrzlpmft give a way to work out a way forward.
But it is the traditions of your field that dominate here - whether sensible or not.