I have now read several times that symmetrical facades do not meet with much enthusiasm among experts.
This is a shortened conclusion. Often the usability inside suffers under the dictate of the outer symmetry. Many - including myself - consider that nonsense.
What is the right measure of asymmetry? Golden ratio? Fibonacci sequence?
What makes a building interesting and do you have examples of this?
You apparently have the idea of an ideal-typical schematic approach to the aesthetics of asymmetry. That would interest me as well, although I rather believe that the earth is flat...
There are very many completely different approaches to making a building "interesting". They all have to do with "think first, then act."
Examples:
[*]consistent "form follows function" principle. This presupposes a thorough consideration of the goals the building is to fulfill. Technology is not in the foreground but is not concealed. You can see what each detail is for. What has no function is not there. (look at Bauhaus - after Gropius and associates, not in vendor brochures...)
[*]the opposite: a coherent playfulness in details (examples exist from many style-defining periods - Gothic, Baroque, Renaissance, Victorian, Art Nouveau...)
[*]the representation of the builder’s own style
[*]the communication of the house with its surroundings
[*]a emphasized master feature can set a special aesthetic appeal
[*]recurring themes of design in form, material, and color can form an exciting arc
[*]an interplay between straightforward symmetry and a pronounced break at a prominent spot
[*]...
Of course, I planned my extension perfectly symmetrically.
I do not understand the word "of course" in this sentence. Symmetry changes its appearance in relation to the environment and changing viewing angles. If it is possible to integrate these aspects into a symmetrical arrangement, the house will certainly emanate fascination. Mere vertically axis-symmetrical frontal views are not enough for that.
If that brings you joy exactly as it is, that is good. If you also want to give your house something special for the eyes of others, that is not enough – and an architect can only help if his creativity is given space and is not restricted by many fixed guardrails from the client.