Because once they come in sufficient numbers they will turn your country into the country they fled from - and then you are in trouble.
Also the US and Western European countries are in much better economic and civic conditions that the immigrants can take advantage of to live better lives and contribute.
Regardless, the culture is that of a nation of immigrants. I don't see how anything here can cause major cultural shift away from that. I am willing to bet you won't be willing to elaborate either, so next goal post move please...