Very few animals 'play' or engage in any form of recreation that might indicate their basic cognitive ability stretches beyond breeding and eating.
That suggests to me you should spend more time observing more animals. There is plenty of evidence to the contrary across a wide range of species.
I'm personally not a big fan of the overall concept most have when the word "pet" is used, either - it offends me deeply - like in your context there is some concept of ownership. This is entirely wrong, the only thing you "own" would be a responsibilty and duty of care. The animal should want to be there, with you. Any other setup just isn't worth having. People would often question how my dog was trained so well, never attached to string ever, being left unattended outside whilst shopping, responding to handsignals for hunting or crossing the road etc - it was simple. It wanted to be where I was and it wanted to make me happy because it had the best life a dog could possibly have.
I'm not suggesting the local cattle farm be transformed into some politically correct wonderland centric to the rights of cows, nor do I think this requires specific mention in the constitution, life is life it shouldn't matter what type or where it is. All that should be required is just a measure of consideration for sentience. It might be of "another level", but it can still think. The emotional context is differing but it can still feel. Animals of most species commonly exhibit individual "personalities". I am personally of the opinion that if you would think purely by the fact of your "human" status you would be attributed some sort of "right" that is above that of, or additional to another you've just demonstrated that clearly you are not deserved. On the subject of rights, generally, far too many think they have some sort of right to life due to the random probability of their existence. Life is not a right, it is a privilige - and one that can and will be revoked at any second. There should be more appreciation and less expectation along with the recognition that this within itself isn't anything special.