I don't think this song is actually about his dog. My guess is the "someone he used to love" is the person taking the picture of him with his dog. There's someone off-camera making him laugh. When he sees the pictures he remembers something someone who wasn't there can't see, thus "don't yell at me cause you can't see who I am thinking of." The death of his pets is just symbolic of the way the past fades and the only thing left are memories/photos.
I don't think this song is actually about his dog. My guess is the "someone he used to love" is the person taking the picture of him with his dog. There's someone off-camera making him laugh. When he sees the pictures he remembers something someone who wasn't there can't see, thus "don't yell at me cause you can't see who I am thinking of." The death of his pets is just symbolic of the way the past fades and the only thing left are memories/photos.