If humans have souls then animals probably do too. We evolved from animals after all.
As the most successful and intelligent species on Earth, we like to think we're special or distinct from the animals. This is an egotistical belief. Our morality, love, and altruism may appear special, or even `divine', but there are rudimentary versions in the animal kingdom.
There's no evidence for souls, but there's plenty of evidence that we desire some kind of eternal life. All species fear death, but only one appears to have the episodic memory and imagination that is necessary to create an afterlife belief to soothe its existential anxieties.
To think that humans have souls and animals don't, you'd need to be an egotist and a slave to wishful thinking.... or just religious