Why don't airlines fly a straight line between Barcelona and Düsseldorf?

Flight routing in Europe is actually quite interesting. Eurocontrol, which controls all the airspace, has an algorithm which either accepts or rejects a route you submit but many times routes are rejected for non obvious reasons.

Due to this, most people use third party software which generates routes and does a brute force search on the Eurocontrol system until one is accepted. When you go ahead and actually fly the routes though, it is pretty common for ATC to give you shortcuts between most sectors.