Earlier quoted context omitted.
I can't understand that rethoric. You get a new consumer as well, so you have merely increased the population.
The belief that economics is a zero-sum game is sadly quite prevalent.
It's about supply and demand.
If you supply labor at X skill level, an influx of immigrants at X skill level (but not of Y or Z skill level) will reduce the buying power of your wages.
Taking it to real life - people tend to oppose immigration when they are at X skill level, and support it when they are at Y or Z skill level. It's raw self-interest often dressed up as altruism or principle.
You can see this understanding here whenever H1B is discussed - suddenly supply and demand becomes an obvious economic concept.