We are all immigrants, it says. It looks like a proposition in a syllogism, which, in its informal form, presumably goes something like this: since I am an immigrant, or some of my ancestors were immigrants, therefore what right do I have to oppose someone else becoming an immigrant too? Rather, I should welcome new immigrants.
This is a very shaky logic though (as pretty much all slogans have). Take a stupid thought experiment of a lifeboat that is leaving a sinking ship. There are only so many passengers that it can carry. All of its passengers are passengers. Yet, it does not follow that since all passengers are passengers they should allow other people (potential passengers) to board the boat ad infinitum (to also become passengers). At some point the boat will be filled to its capacity, so no-one else will be taken.
There are numerous less dramatic examples where this logic (you are X, therefore shame on you if you do not allow another to also become X) does not work. It must be obvious, mustn’t it? So why is this slogan so popular?