Even through animal are in the same existence as human why is animal a lower realm than paitrya realm in Five Destinations?
Do you mean preta? Ghosts?
If that’s it, when you read the Petavatthu you can see that there are many ghosts that even on their own experience deva-like happiness. And when people share merit with them they especially experience deva-like happiness.
But I’m not aware that there is a specific reason given in the suttas.
Even though they exist together, the animal realm is lower than the human here and now, and it would be unwise for humans to attribute to it a higher realm:
“Here, Punna, someone develops the dog duty fully and unstintingly, he develops the dog-habit fully and unstintingly, he develops the dog mind fully and unstintingly, he develops dog behavior fully and unstintingly. Having done that, on the dissolution of the body, after death, he reappears in the company of dogs. But if his view is such as this: ‘By this virtue or duty or asceticism or religious life I shall become a (great) god or some (lesser) god,’ that is wrong view in his case. Now there are two destinations for one with wrong view, I say: hell or the animal womb. So, Punna, if his dog duty is perfected, it will lead him to the company of dogs; if it is not, it will lead him to hell.”—Majhima Nikaya 57
AN 10.177 is about this subject matter.