Why nude in the sauna?

Lately we have been to a hotel sauna and steam bath in Düsseldorf, Germany. As northern Europeans, we took off all our clothes as it is required to German sauna etiquette. However, there have been some people from abroad not understanding this. They left their bathing costumes on and seemed to be embarrassed by the other people’s nudity. 

(Picture below: sign in a Swiss SPA)

Who is wrong? Why is it required to take off clothes?