How do I phrase (in my thesis) that results in an important study are wrong? The title probably comes off wrong, I tried to keep it short. I do not necessarily want to make an absolute statement like "that is wrong". But I do need to address the problems I am facing with a study that is important for my thesis.

There is a relatively influential paper which I have used again and again in my studies, and it shows many very interesting experimental results. I could successfully recreate most of those results, and my research is based on them. However, there is one result where I have to conclude that it is basically nonsense. I have repeated the exact measurement again and again and could never recreate their result. With my new theoretical knowledge I can also safely say that the result shown in the paper makes no sense and has to be wrong, while the one I get from my own measurements makes perfect sense.

So my research means that a result that was described as useful and interesting in this paper is wrong, and therefore not useful. My plan was previously to do multiple studies based on it, and now I want to make clear why that is not possible. So I need to show that their results are wrong, and mine are correct, and I need to explain why that is so.

I have the facts on my side, but I just cannot think of a way to do this in a professional manner. I do not want to sound like I'm reveling in a "gotcha" moment, and I do not want to step on anyone's toes. I just want to make clear that this particular topic is a dead end.

I want to address this in my "Discussion" section of this chapter. I would be grateful for ideas how to approach this. Should I give them the benefit of doubt? I worry that this will water down my own results, which are directly opposed to theirs. Should I think of other potential explanations, like "maybe what they show is a measurement artifact", or will that come off as condescending?
I think you can be pretty straightforward, especially in a thesis.  Describe the experimental disagreement first (amount of it and number of measurements in your study versus the earlier work).  Next para, state that theoretical considerations also support your measurements versus the earlier study (~amount of difference and explication of the theory rationale).