Even flowers are protected by the law in some cases.
When you're saying "grant them rights" you're really saying "let my dog vote for a US president", "let my dog go to school like other humans do" and "let my dog have a fair trial". It's ridiculously absurd. Dogs aren't persons. The people you've referred to who suffer mental disorders are still people, even if their IQ is lower they're still more intelligent and more emotional than dogs are. As to newborns, they grow up to become people - so there's your difference.