Christians have always understood that human beings are like other animals at the physical level. This is stated very frankly in the Bible:
“[A]s one dies, so dies the other. They all have the same breath, … . All are from the dust, and all turn to dust again.” Ecclesiastes 3:19-20
What makes human beings special, however, is that we also have a “spiritual” dimension, which transcends the physical and biological. According to Christian tradition, what makes humans “spiritual” is that we have reason and free will, and it is because of these two powers, pre-eminently, that we are said to be made “in the image of God.” In the words of the Catechism of the Catholic Church,
“By virtue of his soul and his spiritual powers of intellect and will, man is endowed with freedom, an ‘outstanding manifestation of the divine image.’” (CCC 1705)
Because human beings are rational and free, we are capable of love:
“Being in the image of God, the human individual possesses the dignity of a person, who is not just something, but someone. He is capable of self-knowledge, of self-possession and of freely giving himself and entering into communion with other persons. And he is called by grace to a covenant with his Creator, to offer him a response of faith and love that no other creature can give in his stead.” (CCC 357)
The powers of rationality and freedom cannot be completely accounted for in terms of physical, chemical, and biological processes — a conclusion that is supported by strong philosophical arguments. That is why the Church teaches that the “spiritual soul” of every human being is not simply transmitted biologically from parent to child but is directly conferred by God.
“[E]very spiritual soul is created immediately [i.e. directly] by God — it is not ‘produced’ by the parents.” (CCC 366)
In other words, human beings have a nature that is both physical and spiritual, with the physical arising from matter and the spiritual transcending matter and coming from above. This is symbolized in the Book of Genesis by the first human being (“Adam”) being formed “from the dust of the ground,” and then being “breathed” upon by God. That is how the Church has interpreted Genesis 2:7 from ancient times until today (see CCC 362).
This is perfectly consistent with the idea that at the physical level human beings arose through a gradual process of biological evolution from other, non-rational animals, from whom we also derive those mental capacities that we have in common with them, such as sensation, memory, emotions, etc. Understood in this way, biological evolution and the “abiogenesis” which preceded it were just the natural processes through which the “dust of the ground” was gradually formed over eons into the vast diversity of living things that have existed throughout history, in accordance with God’s eternal plan. At some point, however, there was a “transition to the spiritual” that went beyond such processes, with God acting in a special way to raise one earthly species to the level of rationality and freedom, enriching but not in any way destroying our animal inheritance.
Resources for further study
Religious Faith Meets Modern Science, Paulinus F. Forsthoefel, S.J. (Alba House, 1994), Chapter 5 (“Adam and Eve: Our First Parents, Monogenism and Polygenism”), Chapter 10 (“The Evolution of Man”), and Chapter 11 (“The Uniqueness of Humans”).
Faith, Science, and Reason: Theology on the Cutting Edge (2nd edition), Christopher T. Baglow (Midwest Theological Forum, 2019), Chapters 9 and 10.