I don't doubt that animals have emotions. I wonder if they have the same scope? It could be they have a more limited or a more wide range of emotions.This is why I like Jacques Lacan's notion of "organ without body" to capture the idea of the emotion as an organ which overdetermines the body as a whole (as opposed to the physical organ which is a part within the body).
I don't know much of anything about Lacan, but a cursory glance at his work (wikipedia) seems to indicate he was pretty specifically looking at one particular, male organ. I can't think of any other organ in the body that has the same outsized emotional/mental impact as that organ. But, this organ really becomes a symbol for the outsized systemic effect of arousal. Much like the heart becomes a symbol of love. It's odd that no other organs or body parts have the same type of symbolic definitions. We don't get scared and then say it came from our spleen.