Sometimes, it's important to realize that a decision to help someone in need may have results that far outweigh the benefit to a single person. For example, I learned that in a country I recently visited—one that takes the benevolent position of accepting anyone and everyone into the country no questions asked—a person from a third country brought TB in with them. Now, everyone who was in the office I visited has to undergo testing to see if the disease overtook others.
Considering the economic plight of so many of our neighbors to the south of us, it's easy to simply throw out thoughtless statements about how we should let them all in and give them a chance to better their conditions. But the reality is, every person who comes into the country outside of proper channels presents a threat to the health of millions of others. TB, for example, continues to be a disproportionate problem in border states and counties brought on by the large numbers of people coming into the country without proper screening. And TB is not the worst problem.
When people casually toss around the notion that we should help everyone, they should consider how many may be hurt by a careless attitude about how to do it.