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Depends on the particular Pokemon's perspective and desires.
>Pikachu A: Acts like your common Pikachu, it doesn't talk, doesn't think like humans, doesn't care about things that humans care about or desire. It solely cares about getting stronger through battle, food, having friends, finding a trainer, and eventually finding a mate.
>Pikachu B: Can speak like a human, can understand humans, has human level intelligence, comprehension, wisdom, independence, and desires. It spends its time working, training, learning, and doing exactly what humans do. While it does want to find a mate to have offspring with and battle to stay in shape, even find a trainer to help it, its still wildly independent. It even wants human rights.
>Pikachu C: Mentally incredibly smart, can talk, wise Just like Pikachu B! Yet it doesn't share the same desires and perspectives as Pikachu B. It is comfortable and happy with the life it lives where it simply enjoys learning a little bit on the side while its primary goal is to still battle, grow stronger, make friends, and find a mate.
In instances like this I'd say Pikachu B absolutely should have Human Rights, Pikachu's A & C on the other hand either would have the rights be wasted on them or just not desire them or care about them.