There are those who will use the term "European" and will not be thinking of it as a country. This might occur also when we speak of any continent.
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Fortunately there are very few of you who use the term 'European' when discussing a particular issue. Whats easy to spot is those who partake in this lazy misinformed approach and their attitude to most subjects. An approach that often assigns 'blanket statements', often hugely out of context, to intricate societal problems. European culture, demography and politics should not be lumped into some-kind of homogeneous club. Of course we share similarities at times but at other times our approach will be 'chalk and cheese'.
Paul
The term "Europe" or "Western Europe" might have been used when regarding Muslim problems because most European countries suffer from them to greater or lesser degrees.
If, also, there might be six or so European countries which share a similar problem it is far easier to say European than name all the countries involved. We can say Western Europes, parts of Europe, and so on, but sometimes just the shorthand will have to suffice with the reader having to pick up on the intent,.
I'm sure many use this shorthand for Canada and the the USA also, rather than being specific about the provinces or states involved.
Why any offense is taken at this is not clear, but it sounds very similar to the Elephant Man's cry for individualism.
It is not a big deal. Sometimes people will generalize and quite often those generalizations will have some truth attached to them.