Not a lot of Jews remained in Arab states. about 1% of Jews remained in arab states. Most migrated to Israel. A lot also migrated to France, The US and other places. You can argue about why they left, but you can't argue that they didn't leave. In any case, I think its pretty delusional to look at dozens of communities, some with a thousand years of history in those countries, that went from 10s or 100s of thousands of members to dozens within a decade and reject the possibility that they left because they were persecuted.
Austrian police say they expect 10,000 migrants to arrive from Hungary (DPA)
from the article: Recognize Jews as refugees from Arab countries