But if the representatives are chosen by the, presumably, democratically elected governments how are they "anti-democratic". Unless representative democracies are inherently undemocratic (and therefore most European government themselves undemocratic), I fail to see how this can be described as "anti-democratic".

In basically every democracy there is a way for the elected representatives to push through legislation which is unpopular or only supported by a small portion of the population. But this is an intentional feature.