Because basic human kindness...
...that's why.
When people are fleeing for their lives, one does not slam one's door in their face.
Or were you aghast that America took in Cubans and anyone fleeing the Soviet Union/Warsaw Pact countries?
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And I'm not talking about the majority of 'refugees' that came to Europe last year, as many were from Africa and Afghanistan. Those are not refugees but those seeking a better life for themselves and their families - ie: normal immigrants.
Those get handled by standard means.
Those were not 'normal' immigrants. Only 30% of those could be described as 'families', the rest were service age males.
An old west litmus test was the presence of women and children in the group in what would be considered to be ordinary numbers. If they were absent, the probability of the group being a war party or a raiding force was significantly higher. If the women and children were there, they may have been hunting or just moving camp.
If it was not for taqiya, being Christian could be one check for refugee status.
The grim reality is that mixed in with those who claim to be fleeing repression (and many are) are the few who have malignant intent.
As for the Muslims among them, there will always exist the desire to convert the US to Islam, and achieve the Caliphate. You just can't change that fundamental precept of Islam.
We are already teaching ESL (English as a Second Language) classes, already offering services in languages other than those of our founders, at least written with pretty much the same alphabet. Beyond ordinary tendencies for xenophobia and distrust remains the consideration that relatively few Americans can read the script of arabic nations, any more than they can read chinese or japanese writing. At least, at present, neither the Chinese nor Japanese are looking to subjugate entire populations based on religious considerations, but in any of those languages, posters could be put up announcing the time and date to blow up your neighbor and most people would be oblivious to the announcement they just could not read. A website which appears to be absolutely friendly could post 'jihad day' in the corner or a sidebar ad, and what average American would know? It is a 'code' in plain sight, even without idioms and euphemisms.
Look to the enclaves of Somalis in the Minneapolis/St Paul vicinity, and Islamic enclaves elsewhere, and you will see there is often little desire to assimilate, to become "American", and this adds to the significant burden we already have of people who do not comprehend our Constitution, Founding Documents, the philosophy behind them, nor do they really care except to invoke them to get special considerations. We see this everywhere from Dearborn, MI to Paris, France, and it has tremendous potential for or already causes problems, as those enclaves become ruled by de facto Sharia law as they become no-go zones for LEOs.
With the assimilation problem we already have, I think we should look at the way other countries handle immigration: What skills do the potential immigrants have? Can/have they been vetted, insofar as hostile intent/actions/tendencies toward America and Americans?
What is the potential that they will become 'radicalized' while here? What problems have they had? How do/can we avoid that here?
The obvious answer is to not bring it here, and thus not have to 'cure' it.
Would you want them living next door? On all sides? Not just in some other town far away, not even just across town?
If we can't find good answers to those questions, why let them in until we can? After all, the entrance of potential terrorist elements (beyond mere drug cartels and that associated violence and the Communist/Socialist agitations of the La Raza set) through our southern border is an issue which has been raised in conjunction with the illegal immigration issue (Although it seems the average Mexican male can grow a better looking beard, the hostiles blend in nicely) and has been a main impetus for securing that border, beyond the obvious problems of drug importation and crime.
Immigration has gone from accepting a few to the death of a thousand cuts, between those who won't assimilate, to the load on LEOs, social and other services, and the general drag on the economy. Allowing time for the current situation here to be sorted out and those present to assimilate and learn English is a good idea. While there are those who genuinely are threatened, they have options other than the US as well, and we can far better afford to be picky about who we let in.