What is the primary reason for these prohibitions?

The first thing to understand is that all dense matter—human bodies, the bodies of all terrestrial and aquatic animals, and the bodies of all plants—are masses of inert material elements. They are composed of earth, water, fire, air, and ether, and owe their existence to the spiritual souls that reside within them.

Indeed, it is the spiritual souls residing in the specific physical body, bestowed upon them according to their karma, that give life to the body. Remove the soul from the body, and the latter becomes inert, dead. It is therefore the soul that gives life to the body and allows it to move.

This is why it is forbidden to kill anyone—human beings, land and aquatic animals, and also forbidden to destroy plants—because within each of these various bodies resides a soul, as well as God, in His form as the Supreme Soul, who accompanies the incarnate spiritual being throughout their earthly existence.

It is therefore forbidden to kill anyone—human, animal, or plant—because it hinders, or even stops, the spiritual evolution of a soul. We do not have the right to prevent a soul from continuing its spiritual evolution.

In truth, preventing a soul from continuing its spiritual evolution exposes us to a severe and deserved punishment.

Krishna condemns those who kill animals and dare to eat their flesh, as He expresses through this reflection to an offender: You must have committed the offense of slaughtering animals, in hunting or in the course of your policy. To regain your purity, simply indulge in the practice of devotional service and keep your mind constantly absorbed in Me. Near is the time when you will be for eternity free from the consequences of these sordid acts.

To serve Krishna, the Supreme Person, with love and devotion is the only value by which it is possible to gain the favor of the Sovereign Lord, it is the only way that leads to ultimate success in God-consciousness.