Your body is yours but you are not of your body as body is temporary but soul is eternal, there is no paradox in it, just like a painting is drawn by a painter not the vice versa, just like a house is built on land not in sky, similarly one's body and its ambiance is product of all previous birth's collective Karmas. An object is driven by subject, similarly Prakriti/Maya i.e. mind, body, intellect are driven by soul/consciousness also known as Purusha in Samkhya.
Geeta Chapter 2
2.22 As a person sheds worn-out garments and wears new ones, likewise, at the time of death, the soul casts off its worn-out body and enters
a new one.
2.23 Weapons cannot shred the soul, nor can fire burn it. Water cannot wet it, nor can the wind dry it.
2.24 The soul is unbreakable and incombustible; it can neither be dampened nor dried. It is everlasting, in all places, unalterable,
immutable, and primordial.
2.25 The soul is spoken of as invisible, inconceivable, and unchangeable. Knowing this, you should not grieve for the body.
2.27 Death is certain for one who has been born, and rebirth is inevitable for one who has died. Therefore, you should not lament over
Basically, like while playing some modern computer game, one chooses a character but death of character within the game doesnot kill the player in reality, similarly death of physical body does not kill the soul as parting of soul/consciousness from the current body immediately makes object i.e body inert and rotting. Now an animal can never realize its real nature i.e. soul because of lack of intellect, its only in human birth a soul can self-realize its true nature i.e. Moksha and be free from dependency of Maya and need of reincarnation. More explanation of Purusha-Prakriti or Kshetragya-Kshetra.
Geeta Chapter 13
Bhagavad Gita 13.1 Arjun said, “O Keshav, I wish to understand what
are prakṛiti and puruṣh, and what are kṣhetra and kṣhetrajña? I also
wish to know what is true knowledge, and what is the goal of this
Bhagavad Gita 13.2 The Supreme Divine Lord said: O Arjun, this body is
termed as kṣhetra (the field of activities), and the one who knows
this body is called kṣhetrajña (the knower of the field) by the sages
who discern the truth about both.
Bhagavad Gita 13.3 O scion of Bharat, I am also the knower of all the
individual fields of activity. The understanding of the body as the
field of activities, and the soul and God as the knowers of the field,
this I hold to be true knowledge.
Bhagavad Gita 13.5 Great sages have sung the truth about the field and
the knower of the field in manifold ways. It has been stated in
various Vedic hymns, and especially revealed in the Brahma Sūtra, with
sound logic and conclusive evidence.
Bhagavad Gita 13.6 The field of activities is composed of the five
great elements, the ego, the intellect, the unmanifest primordial
matter, the eleven senses (five knowledge senses, five working senses,
and mind), and the five objects of the senses.
Bhagavad Gita 13.7 Desire and aversion, happiness and misery, the
body, consciousness, and the will—all these comprise the field and its
Bhagavad Gita 13.8 – 13.12 Humbleness; freedom from hypocrisy;
non-violence; forgiveness; simplicity; service of the Guru;
cleanliness of body and mind; steadfastness; and self-control;
dispassion toward the objects of the senses; absence of egotism;
keeping in mind the evils of birth, disease, old age, and death;
non-attachment; absence of clinging to spouse, children, home, and so
on; even-mindedness amidst desired and undesired events in life;
constant and exclusive devotion toward Me; an inclination for solitary
places and an aversion for mundane society; constancy in spiritual
knowledge; and philosophical pursuit of the Absolute Truth—all these I
declare to be knowledge, and what is contrary to it, I call ignorance.
Bhagavad Gita 13.13 I shall now reveal to you that which ought to be
known, and by knowing which, one attains immortality. It is the
beginningless Brahman, which lies beyond existence and non-existence.
Bhagavad Gita 13.14 Everywhere are His hands and feet, eyes, heads,
and faces. His ears too are in all places, for He pervades everything
in the universe.
Bhagavad Gita 13.16 He exists outside and inside all living beings,
those that are moving and not moving. He is subtle, and hence, He is
incomprehensible. He is very far, but He is also very near.
Bhagavad Gita 13.17 He is indivisible, yet He appears to be divided
amongst living beings. Know the Supreme Entity to be the Sustainer,
Annihilator, and Creator of all beings.
The four Mahavakyas of Vedanata are also step by step explanation of same reality ending in Anubhava Vakya 'Aham Brahmasmi'.