They're not saying that we should get rid of natural-born folks. They're just saying that often times the people who most want their nation to not allow other folks in, don't appreciate all of the things that those other folks provide for them. i.e. Immigration is subsidizing a lot of the things you probably enjoy about your life, and we should probably be considering it more as a blessing than a curse.
Nobody is trying to replace you. They're just trying to help you, and provide a better opportunity for their children once they've bought into the same system your parents bought into.