The basis for the size-matters pitch is a 2008 study on the impact of phthalates, chemicals used for plastic and personal products. However, the study does not refer to chicken or poultry and the suggestion is that phthalates (which are more commonly used in such as detergents, hair sprays and raincoats) can contaminate poultry through the chicken feed or its packaging.
I understand how these pitches bring notoriety to PETA, which seems entirely driven by a desire for controversy. However, while it may attract donors from the extremes, it paints the entire animal rights movement as wing nuts and wackos. It is a sad legacy of the PETA leadership that they have reduced this organization to virtual graffiti level and trash talking discourse. That says much more about the people running PETA then the animals that needed to be protected.
