If you're a citizen of a European country, you're allowed to cross the border and enter another country, but there's no provision to get protection in that country. The European accord on the common asylum system prohibits the extension of refugee protection to EU national citizens. Somebody who is, for example, of Roma ethnicity and is fleeing persecution will find they not only can't get protection in a neighbouring European state, but they also cannot remain there. That is because capacity to remain is contingent on finding a place within the labour market.
For the group of people who are severely discriminated against, one form this discrimination often takes is labour market discrimination. They cannot get the one thing that will give them the right to remain within that country. Although it is a small number and a small percentage, and although much of Europe is a quite reasonably safe place for most individuals, in cases of severe discrimination the right to remain simply cannot be extended.