The Vedanta Sutras of Badarayana, Commentary by Sankara (SBE38), tr. by George Thibaut  at sacred-texts.com
16. But the designation (as being born and dying) abides in the (bodies of beings) moving and non-moving; it is secondary (metaphorical) if applied to the soul, as the existence (of those terms) depends on the existence of that (i.e. the body).
On account of certain popular modes of expression such as 'Devadatta is born,' 'Devadatta has died,' and the like, and on account of certain ceremonies such as the Gâtakakarman some people might fall into the error of thinking that the individual soul has a beginning, and in the end undergoes destruction. This error we are going to dispel.--The individual soul has no beginning and is not subject to dissolution, since thus only it can be connected with the results of actions, as the Sâstra teaches. If the individual soul perished after the body, there would be no sense in the religious injunctions and prohibitions referring to the enjoyment and avoidance of pleasant and unpleasant things in another body (another birth). And scripture says, 'This body indeed dies when the living soul has left it, the living soul does not die' (Kh. Up. VI, ii, 3).--But it has been pointed out above that ordinary language speaks of the birth and the death of the individual soul!--True; but the terms 'birth' and 'death,' if applied to the soul, have to
be taken in a secondary sense.--What then is that thing to which those words apply in their primary sense, and with reference to which we can speak of a secondary sense?--They apply, we answer, to whatever moves and whatever does not move. The words 'birth' and 'death' have reference to the bodies of moving and non-moving beings; for such beings are born (produced) and die. To them the terms 'birth' and 'death' apply in their primary sense; while they are used metaphorically only with reference to the soul dwelling in them. For their existence (i.e. their being used) depends on the existence of the body; i.e. the words 'birth' and 'death' are used where there take place the manifestation and disappearance of bodies, not where they are absent. For nobody ever observes a soul being born or dying, apart from its connexion with a body. That the words 'birth' and 'death' have reference to the conjunction with--and separation from--a body merely, is also shown by the following passage: 'On being born that person assuming his body, &c.; when he passes out (of the body) and dies,' &c. (Bri. Up. IV, 3, 8). The gâta-ceremony also is to be viewed as having reference to the manifestation of the body only; for the soul is not manifested.--Whether the individual soul is produced from the highest Self like ether, &c. or not, will be discussed in the next Sûtra; the present Sûtra merely states that the gross origination and dissolution which belong to the body do not affect the soul.