In fact we are the Soul inside our body & this Soul can never die though body may die. As per the 'Bhagwat Gita', our body is like our clothes that we wear on our body & after death these worn out clothes are dropped by the embodied Soul. In that sense our body is the Overcoat of our Soul inside. We in essence are a 'Soul' & this 'Soul' of ours shall take another body (read, shall wear another pair of clothes / Overcoat) after death. So this eternal Soul is indestructible which changes its present embodied form/body for another embodied form/body, when the physical body dies.
First one is "Verse - 22, Chapter Two of Bhagwat Gita"
“vasansi jirn-nani yatha vihaay
navani grihnati naro-parani
tatha sharirani vihaya jirnany-
anyani sanyati navani dehi” (Bhagwat Gita: Chapter II verse 22)
"Sri Krishna says to Arjuna: As a person discarding worn-out clothes, puts on new garments, likewise the embodied soul, casting off worn-out bodies,enters into other bodies which are new."
Second one is "Verse - 23, Chapter Two of Bhagwat Gita"
“nainum chindanti shastrani
nainum dahati pavaka
na chainam kledayanty-apo
na soshayati maruta” (Bhagwat Gita: Chapter II verse 23)
"Sri Krishna says to Arjuna: Weapons cannot cut the soul, nor it can be burned by fire, nor water can moisten it, nor wind can make it dry."
Third one is "Verse - 24, Chapter Two of Bhagwat Gita"
akledyo-asoshya ev ch
nity sarv-gatah sthanur
achalo-ayam sanatanah” (Bhagwat Gita: Chapter II verse 24)
"Sri Krishna says to Arjuna: For this individual soul is incapable of being cut; and insoluble, and can be neither burned nor dried. This soul is eternal, constant, omnipresent, unchangeable, immovable and everlasting."
Fourth one is "Verse - 30, Chapter Two of Bhagwat Gita"
"dehi nityam avadhyo-ayam
dehe sarvasy bharat
tasmat sarvani bhutani
na tvam shochitum-arhasi” (Bhagwat Gita: Chapter II verse 30)
"Sri Krishna says to Arjuna: O descendant of Bharata, this soul residing in the bodies of all can never be slain. Therefore you should not grieve for any living being."
Jai Shri Krishna