You can either provide social benefits to your country's poor or you can have open borders. If you try to do both at once, you're providing social benefits to the world's poor, and the amount of benefits you can provide from a given tax base falls through the floor.
Your ancestors genocided the whole continent, if anything that argument is against what you advocate. We're not in the 1700s, people can travel more easily, information travels instantly, what worked 300 years ago doesn't necessarily works now.
I'm all for helping people but you cannot import the world's misery and expect it to be smooth, first because it doesn't solve anything, second because it just doesn't work from a simple demographic point of view.