Peter, I am not involved with ORS itself, am just on OpenStreetMap contributor. But I did see a difference that might explain it:
Reuterstrasse has a couple of tags on it that are bike specific, while Argelanderstrasse does not. The tags are:
cycleway:both = track
cycleway:both:segregated = no
I think the key one is the first. It says (if my understanding is correct) is that in both directions of travel there is a cycleway that is part of the road or maybe right next to the road.
My theory is that the navigation software factors that in and perhaps figures that a cyclist would go faster on it compared to the other pedestrian favoring route.
A second possibility is that the navigation software saw that SchlosStrasse is one way (even though it is tagged that bikes can go the other way) and somehow decided to not let the bike route go against the flow.
A third possibility is the fact that ORS probably still has broken graphs and that somehow that is affecting its route choice.
I think you can test the second theory by putting a destination SE of the intersection it is close too and see what ORS does.
I tried that and it worked. BUT I also moved B slightly closer to intersection and ORS picked a DIFFERENT longer route.
My conclusion: it might be due to the broken ORS graphs. One can’t easily look at the OSM coding to predict what ORS will do.
IGNORE ALL OF ABOVE. I think the problem is with the intersection. There is a weird turn restriction at the intersection that says vehicles can only turn left (SchloStrasse to Kurfrstenstrasse). So this is probably interpreted by ORS to mean bikes can’t go straight. So all routes that the bikes are given come from either the NE or NW towards than intersection. I don’t understand why, but I would bet on this being the answer.
Play around with location of B and look at the distances. You will see it seems to be making correct decisions except for the intersection.