The problem is that when you use a word like "soul" without having any real idea of what it is you look foolish. Pretty simple, really. If you are talking about the Bible's definition of a soul you are talking about "the life of a breathing person or animal, it's blood." Those things exist.
The idea of a soul is more ancient than the Bible. It's the basis of animism, and it applies to any and all objects in nature. Cultural anthropologist Franz Boas, while studying the last primitive civilizations untouched by outsiders (in Canada, the Yukon) discovered that tribes who had no contact with each other shared a primal fear of nature, in and through all of the objects in the world around them. It was common across the cultures that if any person would upset the balance of nature in the smallest way, like stripping the leaves from a plant without putting them to good use (eating them, thatching with them, etc.) then Nature would respond, by visiting them with a fatal snake bite, or some other calamity. That is , any careless or malicious act by a human was given as the explanation for the unpredictable ways nature can behave. Before the Hebrew culture came into existence, animism was the prevailing form of superstition. Evidence of animism is found in the Bible, from the inheritance of the animist pantheon
The Elohim of Gen 1:1, to the talking snake, the voice coming out of the burning bush. etc.
Souls do not exist. They are the invention of religions which perpetuate a mild form of animism. Metazoans are alive at multiple levels. They have living cells, tissues, organs, and systems. But even a hardline Bible thumper won't insist that the cells have souls, that tissues have souls, the organs have souls, and you're not going to hear them say "a digestive system has a soul" even though it can become quite volatile at times.
That leaves it to ignore all of biology and to treat animals (presumably only large vertebrates) as animated by their alleged soul, while in fact they are animated by the cells, tissues, organs and systems not understood or recognized by religions.
But the fact of life in any organism has nothing to do with religious explanations. Life springs from itself, from gametes to zygote and on to the metazoan form encoded in the DNA.