Myth?! "Breathing Walls" What is the truth?

People have also been in my house who only knew that we built a prefabricated house and were amazed by the great "feeling" that such a prefabricated wooden house offers. I let them ramble on a bit longer and then told them that the house is made of concrete.

Thank you .
I would like to leave your first paragraph regarding conspiracy theorists uncommented, I find it a bit nonsense. I did not ask for "superficial" arguments, but for linguistically simplified explanations. In other words: Please no technical language.
What you did further down, however, and I thank you for that. I was able to understand your explanations and I will inform myself about it or follow up with the provider.

Let's turn the tables. Just explain to us why a wooden wall is climate-regulating compared to a target wall.
How does the moisture leave the house?

I could copy and paste from the Klimaholzhaus website, or you can look it up yourself. I am not a construction expert and, as I said, not a physicist, I find the provider’s explanation plausible. If you, or others, can explain to me with plausible arguments why solid wood is NOT climate-regulating, then I am happy to listen. As I said, I am open and willing without any problems to say: "Aha, see? I didn’t know that. Learned something new."

this must be ensured differently (ventilation system, airing, ...).

By the way, that is also a good point. Maybe one has to air regularly instead? I don't know, I can't remember the provider mentioning that. I will follow up.
When we were at my wife's uncle and aunt's place, I never saw them open the windows (and they sometimes stay there for hours with several people). But of course, I cannot rule out that they do it before or after. I will ask them about it.

By the way, that is also a good point. Maybe you have to ventilate regularly instead? I don't know, I can't remember the provider mentioning that. I will follow up. When we were at my wife's uncle and aunt's place, I never saw them open the windows (and they were sometimes there for hours and with several people). But of course, I can't rule out that they do it before or afterwards. I will ask them about it.

The provider is obliged to provide you with a ventilation concept.

Well, how is sufficient moisture supposed to pass through a solid wood wall? Physically, that cannot work. And as already explained, (little) air doesn’t pass through either, which is not allowed in new buildings. I don’t understand at all how anyone can come up with the idea that a solid wood wall can exchange moisture in significant amounts.

Tego explained that really well.

Please copy what the manufacturer promotes on their site.

And yes, you simply have to ventilate. That’s the only way.
The disadvantages are:
- Effort (ventilating twice a day in a two-story single-family house is annoying)
- Air still often gets stale (a ventilation system simply provides fresh air continuously)
- Higher heat loss in winter (not with controlled residential ventilation because of the heat exchanger, but it does use some electricity)

Modern houses are airtight and this is measured. Breathable walls that should ensure sufficient air exchange would therefore fail any Blowerdoor test.

If I remember correctly, a diffusion-open wall can balance about 3% of the humidity generated in the house. That is too little.