People are status conscious. They care about their rank in society’s pecking order and being at the bottom is bad news. Some lefties argue that only inequality within a society is important not between societies (this allows them to maintain strict immigration controls and argue that nice, just societies can be significantly poorer than the US and UK, yay!).
The obvious way to fix this problem is too import lots of people who would be happy to be on the bottom rung of society and unlikely to be able to leapfrog current citizens within a generation. All pre-immigration citizens would immediately have their relative social status improved. Their wages may decrease slightly, but that should be compensated for by the satisfaction gained by suddenly earning more than others.
The trouble with this is that some immigrants work really hard which means they earn more than “natives”. Not only do these people not help the status of natives, they probably make them feel bad, “why does he earn more than me when he can’t speak English and never went to school?”