However, the Ohr Hachaim continues to tell us, that much more is expected of man, for he is far greater than a beast from the field, using the words of the possuk וּמוֹתַר הָאָדָם מִן הַבְּהֵמָה אָיִן - man is more than the animal. Indeed, Hashem also created us with a Yetzer Hatov, an ability to choose to do what is right and good. We have the seichel, the unique wisdom, and understanding granted to man, to choose the correct path. Therefore, we are expected to constantly strengthen ourselves and rise above our evil inclination.
Thus, although Hashem promised not to completely destroy the world or humanity as a result of their sins, they will still bear responsibility for their actions and be punished accordingly. For although we are רַע מִנְּעֻרָיו, evil from youth, we also possess the ability to choose good; therefore, the Ohr Hachaim cautions us to disgrace evil and rather follow the path of truth.
(רמב''ן ואוה''ח ח כא ד''ה כי יצר)
The רבינו בחיי in his preface to Parshas Kedoshim (ויקרא יט ב) explains the possuk כִּי יֵצֶר לֵב הָאָדָם רַע מִנְּעֻרָיו to mean that a man was born with an animalistic nature; at his core man is comparable to an animal. If he follows his base instincts and pursues his natural desires, he is indeed no more than an animal.
However, despite being inherently similar to an animal, he was also endowed with something much holier, as the possuk says וַיִּפַּח בְּאַפָּיו נִשְׁמַת חַיִּים (בראשית ב ז). Hashem 'blew' into Adam a neshama, a spiritual power from the highest source, which he can use to overcome his animalistic nature.
The רבינו בחיי explains that during creation Hashem created celestial beings who are wholly spiritual, as well as earthly creations which are only physical. Man, however, was created from a combination of both. He possesses both a נֶפֶשׁ הַבְּהֵמִית, an animalistic component, as well as a נֶפֶשׁ שִׂכְלִי, a higher spiritual being which is inherent in the wisdom of man. He adds that a person has the power to use his נֶפֶשׁ שִׂכְלִי in order to completely nullify his נֶפֶשׁ הַבְּהֵמִית, his physical desires, and thus become a solely spiritual being, just like a malach.