Hi Yaro,
I can give you the traditional Jewish answer to this question.
It seems that only mankind has a soul because only mankind is able to choose to do good and evil, below is a jpeg of a commentary on Genesis 1 and a Rabbi's remarks after it.
7: formed. The Heb. is vayyitzer from the same root, yatzar, as is used of the potter moulding clay into a vessel, possibly to remind us that man is " as clay in the hands of the Potter." The Rabbis point to the fact that in this verse the word for " formed " is written with two yods, whereas in v. 19 when relating the creation of animals, it has only one yod. Man alone, they declare, is endowed with both a Yetzer tob (a good inclination) and a Yetzer ra (an evil inclination); whereas animals have no moral discrimination or moral conflict. Another explanation is, man alone is a citizen of two worlds; he is both of earth and of heaven.
I hope this helps.
Brian.