We did receive feedback indicating this line is unclear:
At this time, there simply is no magic argument that will convince everyone – or even a majority – to go vegan.
So I've added this postscript:
To be clear: the point is not that we must use multiple arguments to reach different people. Rather, for the majority of people today, there is no argument at all that will convince them to go vegan.
For the reasons discussed [in the main article – e.g., the chain example], trying to use multiple arguments (even if they were valid) makes us less effective advocates with the people who actually are open to making changes for the animals. Furthermore, as disussed in some of the links [in the main article] (and here and here), many of these arguments can do active harm to the animals, when their overall net impact is assessed. Again, these arguments often reinforce the idea that everyone should be motivated only by self interest, and lead enough people to change from eating large animals to smaller animals to more than offset the good of those who do change for non-cruelty-related reasons.
Therefore, we must always assess the total impact of our advocacy on all animals – not just whether an argument sounds good to us or a few individuals we happen to know. Regardless of how a story, study, or claim sounds to us, if there is any chance it could lead non-vegetarians to eat more chickens and/or fish, we should not promote it.