Question

Why is it difficult to determine which countries belong to Europe and which belong to southwest Asia

Answer 1

The difficulty arises from few different factors:
- Culture
- Religion
- Geography
- Politics

Europe and Asia are actually one continent, but it has been 'divided' into two continents because of the reasons mentioned above. 
Geographically are used some points as zone of separation, but there's still discussion which of the two prevailing is the most relevant.
From cultural and religious point of view Europe and Asia are mostly divided at the border of the Christian and Muslim world, but not totally, which also makes confusions.
And for last we have the political factor, where the geopolitical interest makes superficial borders as zones of interest, and thus making imaginary border lines.