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"Pigs are smarter than a three-year-old child."
They ground the defense of animals in faith, affection or hierarchy, not in sentience.
Why it is weak
The comparison is widely shared but rests on weak studies. The experiment in which pigs used a mirror to find food has not been replicated, and comparing the intelligence of species by a single measure has no solid basis.
And there's a trap: using intelligence as the argument accepts the other person's criterion. If the pig deserves respect for being intelligent, the chicken and the fish, supposedly less intelligent, would deserve less.
How to say it better
Pigs have real cognitive and social abilities, but what matters is that they feel pain, fear and pleasure. That holds for the pig, the chicken and the fish, however intelligent they are.