Neighbor wants to build a semi-detached house with an offset

I assume that the neighbor is simply taking the opportunity to build a covered terrace.

That may be. It is always sensible to find out what the actual wish is. No one wants an expensive offset just for the sake of the offset. So if it is about privacy screening, you have the possibility to talk about alternative solutions that serve your neighbor's goal and cost you neither money nor nerves. If you are at this point in the conversation, you are no longer discussing the disadvantages of the project against your neighbor's idea, but the joint achievement of both goals. This is also extremely conducive to a good long-term coexistence or living together.

Isn't the blue line in the development plan image the building line?

Is the blue line in the development plan image not the building line?

Building line = obligation to build on this line (usually red)
Building boundary = limits that must not be exceeded but can be undershot (usually blue)

So, just to contribute an opinion here, staggered facades are normal in our residential area. If I estimate, out of 50 semi-detached houses, at least 30 have a stagger. Why? Because the plots are not drawn with a ruler, and I don't find it bad at all; it loosens things up.

PS. What if he wanted to build his semi-detached house larger than yours? You wouldn't be able to prevent that either.

Well, I don't care what he does, I just want to understand why someone wants to spend 30,000 to 50,000 euros more in a more complicated way and then asks if he can insulate on my side, etc.

In the past, people built inefficiently without insulation anyway, so the point was different. And with the offset, both corners of each semi-detached house need separate earthworks and deep strip foundations because the elevation levels towards the street are like that.

In the past, people built inefficiently without insulation anyway,

Is that so? What do you mean by "in the past"? Even 40 years ago, insulation was used, just not with the attached ETICS.