Ocrdu makes good points here:

A baby is less rational a being than an adult chimpansee. Apparently, rationality as a trait has nothing to do with your argument: you are simply defining what you should logically argue.

And a dog. A dog has the cognition of a three-year old human. Also, there are studies done which show advanced reasoning abilities in ravens and crows. and yet again, the cognitive ability and reasoning of cetaceans is well-researched and proven. There are many, many more arguments for animals being more complex than people irrationally accepted in previous history. People hastily concluded no rights for animals out of convenience for claiming right to dominion. The rational animal is the best rationalizer of mistakes.

Aside from the importance of biodiversity to support rational life on this planet, concluding animals should not have rights is hasty reasoning. By the evidence, it makes logical sense to acknowledge we don't know the true capability of animals (and their capacity for emotion and suffering).

If you value rational ability as the highest virtue among humans (as I’ve noticed is common in libertarian philosophy) than you also posit it should be used rationally. There is no logical reason why one should not be at least Agnostic on the ontology of animals and what coud suffice for their ability for rational thought.

As human is ‘the rational animal’ not as a being-in-itself, but requiring that there be a comparison, than the dolphin can be defined via relative intelligence to other animals and have some form of elevated status based on this concept, warranting an assessment of the dolphins relation to man and property.

Regardless:

you should at least define what you consider Rational capacity. You could further the argument you make by adding when people evolved rational thought and examine the relation to rights. I doubt rational thought has a causal relation to human rights; it can be used for or against (of course, it's possible a good, intriguing argument could be made in favour of your point of view. I'm not going there though)

Defining man's rights and values as existing because of 'rational' thought isn't an argument on it's own. Arguing that rational thought be necessary for 'property ownership' is an issue in itself.

Regarding the animal rights analogy, it is an issue of semantics. Animals don't have the concept of owning things, but they do know territory and threats on their bodies, expressed in the way they interact with the world, they have very clear signals (both direct and evidence through their complex social interactions). Animals have constraints which determine their needs for livelihood and future prosperity which affect all living things in their environment (they have living conditions same as humans)

Applicable to current governance models, even wild animals are sometimes considered property for the purpose of law. Some state that all wildlife are the property of the Queen of England here in Canada. Or the property of the commons and Native American people. So there are ways to determine hunting rights, seasons,conservation and poaching. Even if there were no animal rights, there’d be many things inhibiting wildlife-as-resource.By extension Property Rights apply to animals. If you are speaking in abstract terms and theoretical libertarian governments, than your analogy regarding taking animals to court is invalid.

There is no identifiable point in someone's life in which they change into a rational person from a non-rational being.

Yes, there are childhood developmental stages.

Point is: Fuckin' rights animals have rights